Syzygies of Abelian and Bielliptic Surfaces in P^4

Details Syzygies of Abelian and Bielliptic Surfaces in P^4 Syzygies of Abelian and Bielliptic Surfaces in P^4

1996-06-20

arxiv.org/abs/alg-geom/9606013v2

Mathematics

Algebraic Geometry

64 pages, author-supplied DVI file available at http://oscar.math.brandeis.edu/~popescu/dvi/bielliptics2.dvi AmS-TeX v. 2.1

Scientific paper

So far only six families of smooth irregular surfaces are known to exist in P^4 (up to pullbacks by suitable finite covers of P^4). These are the elliptic quintic scrolls, the minimal abelian and bielliptic surfaces (of degree 10), two different families of non-minimal abelian surfaces of degree 15, and one family of non-minimal bielliptic surfaces of degree 15. The main purpose of the paper is to describe the structure of the Hartshorne-Rao modules and the syzygies for each of these smooth irregular surfaces in P^4, providing at the same time a unified construction method (via syzygies) for these families of surfaces.

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