Herbert Lange

## 1. Research papers

1. Moduli spaces of algebraic curves with rational maps, Math. Proc. Camb. Phil Soc. 78, 283-292, (1975).
2. Über die Modulschemata der Kurven vom Geschlecht 2 mit 1, 2, oder 3 Weierstraßpunkten, Journ. reine angew. Math. 227, 27-36, (1975).
3. Modulprobleme exeptioneller abelscher Varietäten, Nachr. Akad. Wiss. Göttingen 4, 36-42, (1975).
4. Produkte elliptischer Kurven, Nachr. Akad. Wiss. Göttingen 8, 95-108, (1975).
5. Über die Modulvarietät der Kurven vom Geschlecht 2, Journ. reine ang. Math. 281, 80-96, (1976).
6. Kurven mit rationaler Abbildung, Journ. reine ang. Math. 295, 80-115, (1977).
7. Normendomorphismen abelscher Varietäten, Journ. reine ang. Math. 290, 203-213, (1977).
8. (with U. Stuhler) Vektorbündel auf Kurven und Darstellungen der algebraischen Fundamenentalgruppe, Math. Zeitschr. 156, 73-83, (1977).
9. (with U. Stuhler) Divisoren von rationalen Schnitten in torsionsfreien Garben und ein Satz von Tango. Arch. Math 30, 146-152, (1978).
10. On stable and ample vector bundles of rank 2 on curves, Math. Ann. 238, 193-202, (1978).
11. The stability degree of a rank-2 vector bundle on P2, Notas e Com. de Matem. 91, Univ. Fed. de Pernambuco (1978).
12. On stable and uniform rank-2 vector bundles on P2 in characteristic p, Manuscr. Math. 29, 11-28, (1979).
13. Remark to ''On stable and uniform rank-2 Vector bundles on P2 in characteristic p'', Manuscr. Math. 32, 407-408, (1980).
14. Invertierbare Untergarben maximalen Grades von Rang-2 Vektorbündeln auf der projektiven Ebene, Archiv Math. 34, 313-321, (1980).
15. Universal families of extensions, Journ. of Alg. 83 , 101-112, (1983).
16. Zur Klassifikation von Regelmannigfaltigkeiten, Math. Ann 262, 447-459, (1983).
17. (with M. S. Narasimhan) Maximal subbundles of rank two vector bundles on curves, Math. Ann. 266, 55-72, (1983).
18. Compactified commutative algebraic groups as intersection of quadrics, Publ. Mathém. de l'Université Pierre et Marie Curie, 58, V1-V41, (1983).
19. On elementary transformations of ruled surfaces, Journ. reine ang. Math. 346, 32-35, (1984).
20. Higher secant varieties of curves and the theorem of Nagata on ruled surfaces , Manuscr, Math. 47, 263-269, (1984).
21. (with F. Knop) Commutative algebraic groups and intersection of quadrics, Math. Ann. 267, 555-571, (1984).
22. (with G. Martens) Normal generation and presentation of line bundles of low degree on curves. Journ. reine ang. Math. 356, 1-18, (1985).
23. (with W. Ruppert) Complete systems of addition laws on abelian varieties . Inventiones Math. 79, 603-610, (1985).
24. Höhere Sekantenvarietäten mit Anwendungen für Vektorbündel auf Kurven, manuscr. math. 52, 63-80, (1985).
25. Translations sur les groupes algébriques commutatives, Comptes Rendus Acad. Sc. Paris, t. 300, Sér. I, No. 9, 255-258, (1985).
26. (with G. Martens) Normal generation of line bundles of degree 2p-2 on curves, Abh. Math. Sem. Hamburg 55, 69-73, (1985).
27. (with F. Knop) Some remarks on compactifiactions of commutative algebraic groups, Comment. Math. Helvetii 60, 497-507, (1985).
28. (with K. Hulek) Some examples of abelian surfaces in , Journ. reine ang. Math. 363 , 200-216, (1985).
29. Jacobian surfaces in , Journ. reine ang. Math. 372, 71-86, (1986).
30. (with W. Ruppert) Addition laws on elliptic curves in arbitrary characteristics. Journ. of Algebra 107, 106-116, (1987).
31. Families of Translations of Commutative Algebraic Groups, Jour. of Algebra 109, 260-265. (1987).
32. Abelian varieties with several principal polarizations. Duke Math. Journ. 55, 617-628, (1987).
33. Equations for endomorphisms of abelian varieties. Math. Ann. 280, 613-623, (1988).
34. (with K. Hulek) The Hilbert modular surface for the ideal and the Horrocks-Mumford bundle, Math. Zeitschr 198, 95-116, (1988).
35. (with M.S. Narasimhan) Squares of ample line bundles on abelian varieties. Expos. Math 7, 275-287, (1989).
36. A remark on the degrees of communicative algebraic groups. Illinois Journ. of Math. 33, 409-415, (1989).
37. (with Ch. Birkenhake and D. van Straten) Abelian surfaces of type (1,4). Math. Ann. 285, 625-646, (1989).
38. (with D. Eisenbud, G. Martens and F.-O. Schreyer) The Clifford dimension of a projective curve. Comp. Math. 72, 173-204, (1989).
39. (with Ch. Birkenhake) Cubic theta relations, Journ. reine ang. Math. 407, 167-177, (1990).
40. (with Ch. Birkenhake) Symmetric Theta Structures, Manuscr. Math. 70, 67-91 (1990).
41. (with. Ch. Birkenhake) Norm-endomorphisms of abelian subvarieties. In Classification of Irregular Varieties Proceedings, Trento 1990 SLN 1515.
42. (mit. Ch. Birkenhake) The exponent of an abelian subvariety, Math. Ann. 290, 801-814 (1991).
43. (with Ch. Birkenhake and S. Ramanan) Primitive line bundles on abelian threefolds. Manuscr. Math. 81, 299 - 310.(1993).
44. (with Ch. Birkenhake) Fixed-Point Free Automorphisms of Abelian Varieties. Geometria Dedicata 51, 201 - 214 (1994).
45. Abelian surfaces in , Archiv der Mathematik 63, 80 - 84 (1994).
46. (with Ch. Birkenhake) A Family of Abelian Surfaces and Curves of Genus Four, manuscr. math. 85, 393 - 407 (1994).
47. (with Ch. Birkenhake) Moduli spaces of Abelian Surfaces with Isogeny, Proceedings of the Conference Geometry and Analysis'', Tata Institute Bombay; Oxford Univ. Press (1995).
48. (with E. Sernesi) Quadrics containing a Prym-canonical curve, Journal of Algebraic Geometry 5, 387 - 399 (1996)
49. A vector bundle of rank 2 on , J. London Math. Soc. (2), 583-598 (1998).
50. (with Ch. Birkenhake) Parameter Spaces of Nondegenerate Complex Tori with Endomorphism Structure; Archiv der Mathematik 70, 153 - 159 (1998).
51. (with L. Brambila-Paz) A stratification of the moduli spaces of vector bundles on curves; Journal f. d. reine und angewandte Mathematik 494, 173 - 187 (1998).
52. (with Ch. Birkenhake and V. Gonzalez) Automorphism groups of 3-dimensional complex tori; Journal f. d. reine angew. Mathematik 508, 99-125 (1999).
53. (with Ch. Birkenhake and V. Gonzalez) Automorphisms of 3-dimensional abelian varieties; Contemporary Mathematics, 240, 25 - 47 (1999).
54. (with Ch. Birkenhake) The dual polarization of an abelian variety; Arch. d. Math. 73, 380 - 389 (1999).
55. (with D. Avritzer) <media 5271 - - "TEXT, dan1, dan1.ps, 411 KB">Pencils of quadrics, binary forms and hyperelliptic curves </media> ; Comm. in Algebra, 28, 5541-5561 (2000).
56. Hyperelliptic varieties. Tohoku Math. J. 53, 491-510 (2001).
57. (with D. Avritzer) <media 5311 - - "TEXT, ag, ag.ps, 238 KB">The Moduli Spaces of Hyperelliptic Curves and Binary Forms </media> ; Math. Zeitschr. 242, 615-632 (2002).
58. (with E. Sernesi) <media 5321 - - "TEXT, edoardo1, edoardo1.ps, 311 KB">Severi varieties and branch curves of abelian surfaces of type (1,3) </media> ; Intern. Journ. of Math. 13, 227-244 (2002).
59. (with D. Avritzer) Curves of genus 2 and Desargues configurations ; Adv. Geometry 2, 259-280 (2002).
60. (with Ch. Birkenhake) An isomorphism between moduli spaces of abelian varieties ; Math. Nachrichten 253, 3-7 (2003).
61. (with E. Sernesi) <media 5309 - - "TEXT, e, e.ps, 289 KB">Curves of genus g on an abelian variety of dimension g </media> ; Indag. Mathem., N.S. 13 (4), 523-535 (2003).
62. (with P. Newstead) <media 5279 - - "TEXT, new, new.ps, 333 KB">Maximal subbundles and Gromov-Witten invariants </media> ; in: A Tribute to C.S. Seshadri, Birkhäuser Verlag (2003).
63. (with S. Recillas) Abelian Varieties with Group Actions ; Journ. Reine Angew. Mathematik, 575, 135-155 (2004).
64. (with E. Sernesi) <media 5291 - - "TEXT, LS4, LS4.ps, 242 KB">On the Hilbert scheme of Prym varieties </media> ; Annali di Matematica, 183, 375-386 (2004).
65. (with S. Recillas) <media 5317 - - "TEXT, s1, s1.ps, 224 KB">Poincaré's reducibility theorem with -action </media> ; Bol. Soc. Mat. Mexicana, 10, 43-48 (2004).
66. (with S. Recillas) Prym Varieties of Pairs of Coverings ; Adv. Geometry 4, 373-387 (2004).
67. (with P. Newstead) <media 5285 - - "TEXT, genus0, genus0.ps, 328 KB">Coherent systems of genus 0 </media> ; Intern. Journ. Mathematics, 15, 409-424 (2004).
68. (with S. Recillas and A. M. Rojas) <media 5319 - - "TEXT, LRR4, LRR4.ps, 411 KB">A family of Prym-Tyurin varieties of exponent 3 </media> ; Journ. of Algebra 289, 594-613 (2005).
69. (with P. Newstead) Coherent systems on elliptic curves ; Intern. Journ. of Mathem. 16, 787-805 (2005).
70. (with P. Newstead) On Poincaré bundles of vector bundles on curves ; Manuscr. Math. 117, 173-181 (2005).
71. (with D. Avritzer) Desargues configurations via polar conics of plane cubics ; Geometria Dedicata 120, 59-72 (2006).
72. (with P. Newstead) On Clifford's Theorem for Rank-3 Bundles ; Rev. Matem. Iberoamericana 22, 287-304 (2006).
73. (with S. Recillas) <media 5277 - - "TEXT, sevin5, sevin5.ps, 322 KB">Polarizations of Prym varieties of pairs of coverings </media> ; Arch. der Mathem. 86, 111-120 (2006).
74. <media 5275 - - "TEXT, ppol, ppol.ps, 306 KB">Principal polarizations on products of elliptic curves </media> ; Contemporary Mathematics 397, 153-162 (2006).
75. (with P. Newstead) Coherent systems of genus 0 II: Existence results for k geq 3 ; Intern. Journ. of Mathem. 18, 363-393 (2007).
76. (with D. Avritzer) Moduli spaces of quadratic complexes and their singular surfaces ; Geometria Dedicata 127, 177-197 (2007).
77. (with E. Sernesi) Some Remarks on Symmetric Correspondences ; Abh. Math. Sem. Univ. Hamburg 77, 97-108 (2007).
78. (with C. Pauly) <media 5325 - - "TEXT, fd, fd.ps, 437 KB">On Frobenius-destabilized rank-2 vector bundles over curves </media> ; Comment. Math. Helv. 83, 179-209 (2008)
79. (with P. Newstead) <media 5295 - - "TEXT, genus03rev, genus03rev.ps, 400 KB">Coherent systems of genus 0 III: Computation of Flips for k=1 </media> ; Intern. Journ. of Mathem. 19, 1103-1119 (2008)
80. (with P. Newstead) Clifford's theorem for coherent systems ; Archiv der Mathem. 90, 209-216 (2008)
81. (with V. Kanev) Polarization Type of Isogenous Prym-Tyurin Varieties ; Contemp. Math. 465, 147-174 (2008)
82. (with A. M. Rojas) A Galois-theoretic approach to Kanev's correspondence ; Manuscr. Math. 125, 225-240 (2008)
83. (with E. Izadi and V. Strehl) <media 5323 - - "TEXT, ngonal6, ngonal6.ps, 514 KB">Correspondences with split polynomial equations </media> ; Journ. reine angew. Math. 627, 183-212 (2009)
84. (with A. Carocca, R. Rodriguez and A. Rojas) <media 5315 - - "TEXT, clrr2-v2, clrr2-v2.pdf, 258 KB">Prym-Tyurin varieties using self-products of groups </media> ; Journal of Algebra 322, 1251-1272 (2009)
85. (with A. Carocca, R. Rodriguez and A. Rojas) Products of Jacobians as Prym-Tyurin varieties ; Geom. Dedicata 139, 219-231 (2009)
86. (with Ch. Pauly) <media 5289 - - "TEXT, polarizations2, polarizations2.ps, 558 KB">Polarizations of Prym varieties for Weyl groups via abelianization </media> ; Journ. Europ. Math. Soc. 11, 315-349 (2009)
87. (with P. Newstead) <media 5313 - - "TEXT, csoelrev, csoelrev.ps, 386 KB">Hodge polynomials and birational types of moduli spaces of coherent systems on elliptic curves </media> ; Manuscr. Mathem. 130, 1-19 (2009)
88. (with A. Ortega) Prym varieties of cyclic coverings ; Geom. Dedicata 150 (2011), 391-403.
89. (with A. Carocca, R. Rodriguez and A. Rojas) Prym-Tyurin varieties via Hecke algebras ; Journ. reine angew. Mathematik 634 (2009), 209-234.
90. (with A. Carocca and R. Rodriguez) <media 5281 - - "TEXT, cm8, cm8.ps, 466 KB">Jacobians with complex multiplication </media> ; Trans. of the AMS 363 (2011), 6159-6176.
91. (with A. Carocca, R. Rodriguez and A. Rojas) Prym and Prym-Tyurin varieties: a group-theoretical construction ; Contemp. Math. 510 (2010), 49-60.
92. (with P. Newstead) <media 5297 - - "TEXT, clifford1rev2, clifford1rev2.pdf, 382 KB">Clifford indices for vector bundles on curves </media> ; in: A. Schmitt (Ed.) Affine Flag Manifolds and Principal Bundles. Trends in Math, Birkhäuser (2010), 165-202.
93. (with D. Avritzer and F.A. Ribeiro) Torsion-free sheaves on nodal curves ;  Bull. of the Brazilian Math. Soc.41 (2010), 421-447.
94. (with P. Newstead) Lower bounds for Clifford indices in rank 3; Math. Proc. Camb. Phil. Soc. 150 (2011), 23-33.
95. (with E. Izadi) Counter-examples of high Clifford index to Prym-Torelli ; J. Alg. Geom. 21 (2012), 769-787.
96. (with P. Newstead) Generation of vector bundles computing Clifford indices ; Arch. Math. 94 (2010), 529-537,
97. fileadmin/algeo/users/lange/cliff.pdf(with P. Newstead) Further examples of stable bundles of rank 2 with 4 sections; Pure and Appl. Math. Q. 7 (2011), 1517-1528.
98. (with A. Ortega) <media 5293 - - "TEXT, prym IMRN4, prymIMRN4.pdf, 268 KB">Prym varieties of triple coverings </media> ; Intern. Math. Res Notices 2011 (2011), 5045-5075.
99. (with P. Newstead and V. Mercat) On an example of Mukai ; Glasgow Math. J. 54 (2012), 261-271.
100. (with G. Martens) <media 5332 - - "TEXT, gon1, gon1.pdf, 213 KB">On the gonality sequence of an algebraic curve;</media> manuscr. math. 137 (2012), 457-473.
101. (with A. Rojas) Polarizations of isotypical components of Jacobians with group action; Arch. Math. 98 (2012), 457-473.
102. (with P. Newstead) Bundles of rank 2 with small Clifford index on algebraic curves; in: Geometry and Arithmetic, Series of congress reports, Europ. Math. Soc. Zuerich, 267-281 (2012).
103. (with A. Ortega) Compactification of the Prym map for non-cyclic triple coverings; Intern. Journ. of Math. 24, (2013).
104. (with P. Newstead) Vector bundles of rank 2 computing Clifford indices; Comm. in Algebra 41, 2317-2345 (2013).
105. (with P. Newstead) On bundles of rank 3 computing Clifford indices; Kyoto Journ. of Math. 53, 25-54 (2013).
106. (with Dan Avritzer) Cremona transformations associated to quadratic complexes; Rend. Circ. Matem. di Palermo 62, 27-36 (2013).
107. (with R.E. Rodriguez and A.M. Rojas) Polarizations on abelian subvarieties of principally polarized abelian varieties with dihedral group action; Preprint (2012), Accepted for publication in Math. Zeitschrift.
108. (with P. Newstead) Bundles of rank 3 on curves of Clifford index 3; Journ of Symb. Comp. 57,3-18 (2013).
109. (with P. Newstead) Bundles computing Clifford indices on trigonal curves; Arch. Math. 101, 21-31 (2013).
110. (with A. Ortega) Pryms of non-cyclic triple coverings and log canonical models of the spin moduli space of curves of genus 2; Preprint (2013).
111. (with P. Newstead and Seong Suk Park) Non-emptyness of Brill-Noether loci in M(2,K); Preprint (2013)

## 2. Books

1. (with W.-P. Barth, Eds.) Arithmetic of Complex Manifolds; Proceedings, Springer Lecture Notes 1399, 171 p. (1989).
2. (with Ch. Birkenhake) Complex Abelian Varietes; Grundlehren der Math. Wiss. 302, Springer Verlag, 435 p. (1992).
3. (with W. Barth, K. Hulek, Eds.) Abelian Varieties; Proceedings of the International Conference, Egloffstein, Oct. 1993, de Gruyter, 344 p. (1995).
4. (with Ch. Birkenhake) Complex Tori; Progress in Mathematics No. 177, Birkhäuser, 251 p. (1999). (with Ch. Birkenhake) Complex Abelian Varietes, Second Augmented Edition, Grundl. der Math. Wiss. 302, Springer Verlag, 635 p. (2004).
5. (with Ch. Birkenhake) Complex Abelian Varieties, Second Augmented Edition, Grundl. der Math. Wiss. 302, Springer Verlag, 635 p. (2004).

## 3. Expository and non-mathematical papers

1. On vector bundles of rank 2 on the projective plane Atas da Escola de Algebra , 21-31, Rio de Janeiro, (1978).
2. (with H.J. Brumsack and H. Heinrichs) Emissionen von Stein- und Braunkohlekraftwerken der Bundesrepublik Deutschland; Fortschritte der Mineralogie 62, 97-105 (1984).
3. (with H.J. Brumsack and H. Heinrichs) West German power plants as sources of potentially toxic emissions; Environmental Technology Letters 5, 7-22 (1984).
4. Projective embeddings of Abelian Varieties, Jber. d. Dt. Math. Verein. 93, 161-174 (1991).
5. Some geometric aspects of vector bundles on curves. Aportaciones Matemáticas México 5, 53 - 74 (1992).
6. (with G. Kempf) Theta Functions and Moduli of Abelian Varieties ; in: Selected works of D. Mumford, Springer Verlag 293-308 (2004).
7. Coherent systems on elliptic curves and the projective line; ; Appendix to ''Coherent systems : a brief survey'' by S.B. Bradlow, in Moduli Spaces and Vector Bundles. London Math. Soc. Lect. Note Ser. 359 (2009)
8. Counter-examples to Prym-Torelli of high Clifford index; ; Report of my Oberwolfach talk, June 2010. to appear in Oberwolfach Reports.