Syzygies of Abelian and Bielliptic Surfaces in P⁴

1996/06/20 by Alf Aure, Aure, Alf, Wolfram Decker +7
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #alg-geom #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9606013

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

arxiv created 1997/03/14 · arxiv updated 2009/11/30

Abstract

So far only six families of smooth irregular surfaces are known to exist in P⁴ (up to pullbacks by suitable finite covers of P⁴). 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 P⁴, providing at the same time a unified construction method (via syzygies) for these families of surfaces.

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