2000 character limit reached
The Gauss map for bielliptic Prym varieties
Published 22 Nov 2023 in math.AG | (2311.13521v3)
Abstract: We completely describe the degree of the Gauss map of the theta divisor of bielliptic Prym varieties. We characterize bielliptic Prym varieties whose Gauss degree is the same as Jacobians. We also construct bielliptic Prym varieties with a very low Gauss degree. In dimension $5$, we obtain a complete description of the Gauss degree on the Andreotti-Mayer locus.
- E. Arbarello, M. Cornalba and P. Griffiths “Geometry of Algebraic Curves II” Springer Berlin Heidelberg, 2011 DOI: 10.1007/978-3-540-69392-5
- “Geometry of Algebraic Curves I”, Grundlehren der mathematischen Wissenschaften Bd. 1 Springer New York, 1985 URL: https://books.google.de/books?id=LanxBwAAQBAJ
- Aldo Andreotti and Alan L Mayer “On period relations for abelian integrals on algebraic curves” In Annali della Scuola Normale Superiore di Pisa-Classe di Scienze 21.2, 1967, pp. 189–238
- Arnaud Beauville “Prym Varieties and the Schottky Problem.” In Inventiones mathematicae 41, 1977, pp. 149–196 URL: http://eudml.org/doc/142490
- “Complex Abelian Varieties”, Grundlehren der mathematischen Wissenschaften Springer Berlin Heidelberg, 2004 URL: https://books.google.de/books?id=MOW2gEP7HIkC
- Sebastian Casalaina-Martin “Singularities of the Prym Theta Divisor” In Annals of Mathematics 170.1 Annals of Mathematics, 2009, pp. 163–204 URL: http://www.jstor.org/stable/40345462
- Sebastian Casalaina-Martin “Singularities of theta divisors in algebraic geometry”, 2012 arXiv:1207.1042 [math.AG]
- C.Herbert Clemens and Phillip A. Griffiths “The Intermediate Jacobian of the Cubic Threefold” In Annals of Mathematics 95.2 Annals of Mathematics, 1972, pp. 281–356 URL: http://www.jstor.org/stable/1970801
- Giulio Codogni, Samuel Grushevsky and Edoardo Sernesi “The degree of the Gauss map of the theta divisor” In Algebra & Number Theory 11.4 Mathematical Sciences Publishers, 2017, pp. 983–1001 DOI: 10.2140/ant.2017.11.983
- “Semicontinuity of Gauss maps and the Schottky problem” In Mathematische Annalen 382, 2020, pp. 607–630
- Olivier Debarre “Sur les varietes abeliennes dont le diviseur theta est singulier en codimension 3” In Duke Mathematical Journal 57.1 Duke University Press, 1988, pp. 221–273 DOI: 10.1215/s0012-7094-88-05711-0
- Ron Donagi “The tetragonal construction” In Bulletin (New Series) of the American Mathematical Society 4.2 American Mathematical Society, 1981, pp. 181–185
- Ron Donagi “The fibers of the Prym map”, 1992 arXiv:alg-geom/9206008 [alg-geom]
- William Fulton “Intersection Theory” Springer New York, 1998 DOI: 10.1007/978-1-4612-1700-8
- R. Hartshorne “Algebraic Geometry”, Graduate Texts in Mathematics Springer, 1977 URL: https://books.google.de/books?id=3rtX9t-nnvwC
- David Mumford “Prym Varieties I” In Contributions to Analysis Academic Press, 1974, pp. 325–350 DOI: https://doi.org/10.1016/B978-0-12-044850-0.50032-0
- Juan-Carlos Naranjo “Prym varietes of bi-elliptic curves” In Journal für die reine und angewandte Mathematik (Crelles Journal) 1992.424, 1992, pp. 47–106 DOI: doi:10.1515/crll.1992.424.47
- “Compactifications of the Generalized Jacobian Variety” In Transactions of the American Mathematical Society 253 American Mathematical Society, 1979, pp. 1–90 URL: http://www.jstor.org/stable/1998186
- Constantin Podelski “The boundary of the bielliptic Prym locus”, 2023 arXiv:2312.16591 [math.AG]
- Constantin Podelski “The Gauss Map on Theta Divisors with Transversal A1subscriptA1\mathrm{A}_{1}roman_A start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT Singularities”, 2023 arXiv:2309.09885 [math.AG]
- V V Shokurov “Prym Varieties: Theory and applications” In Mathematics of the USSR-Izvestiya 23.1, 1984, pp. 83 DOI: 10.1070/IM1984v023n01ABEH001459
- Allessandro Verra “The degree of the Gauss map for a general Prym Theta Divisor” In Journal of Algebraic Geometry 10.2, 2001, pp. 419–446 eprint: arXiv:math/9809067
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.
