Canonical surfaces in P^4 and Gorenstein algebras in codimension 2
Abstract
In this paper I investigate minimal surfaces of general type with p_g=5, q=0 for which the 1canonical map is a birational morphism onto a surface in P^4 (so called canonical surfaces in P^4) via a structure theorem for the Hilbert resolutions of the canonical rings of the aforementioned surfaces, viewed as Gorenstein algebras of codimension 2 over the homogeneous coordinate ring of P^4. I discuss how the ring structure of such an algebra is encoded in its resolution. Among other things I show how this method can be applied to analyze the moduli space of canonical surfaces with p_g=5, q=0, K^2=11, thus recovering a result previously obtained by D. Rossberg with different techniques.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 2004
 arXiv:
 arXiv:math/0402369
 Bibcode:
 2004math......2369B
 Keywords:

 Algebraic Geometry;
 Commutative Algebra;
 14J29
 EPrint:
 40 pages