Canonical surfaces in P^4 and Gorenstein algebras in codimension 2

Details Canonical surfaces in P^4 and Gorenstein algebras in codimension 2 Canonical surfaces in P^4 and Gorenstein algebras in codimension 2

2004-02-23

arxiv.org/abs/math/0402369v1

Mathematics

Algebraic Geometry

40 pages

Scientific paper

In this paper I investigate minimal surfaces of general type with p_g=5, q=0 for which the 1-canonical 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 afore-mentioned 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.

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