Equations of (1,d)-polarized Abelian Surfaces
| dc.creator | Gross, Mark | |
| dc.creator | Popescu, Sorin | |
| dc.date | 1996-09-04 | |
| dc.date | 1997-03-05 | |
| dc.date.accessioned | 2026-07-07T09:01:45Z | |
| dc.date.available | 2026-07-07T09:01:45Z | |
| dc.description | We study the equations of abelian surfaces embedded in P^{n-1} with a line bundle of polarization of type (1,n). For n>9, we show that the ideal of a general abelian surface with this polarization is generated by quadrics, and if the embedding is Heisenberg invariant, we give a very specific description of these quadrics. These quadrics are produced using a generalization of the Moore matrices which yields a uniform description of these ideals. We prove that these equations generate the ideals using a degeneration argument, degenerating abelian surfaces to schemes obtained from Stanley-Reisner ideals of certain triangulations of the torus. Furthermore, we obtain information on how to compute the moduli spaces of abelian surfaces of type (1,n) with canonical level structure. In a sequel to this paper, we will study the structure of the equations for n<=9, and also give detailed geometric descriptions for the moduli spaces of abelian surfaces of low degree. | |
| dc.description | 50 pages with 1 figure, author-supplied PostScript file available at http://www.math.columbia.edu/~psorin/eprints/abel-eq.ps (Final version) Plain TeX with epsf.tex and amssym.tex | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9609001 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9609001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/148390 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Equations of (1,d)-polarized Abelian Surfaces | |
| dc.type | text |