Generalized divisors and biliaison

By Robin Hartshorne. 2003

77 citations recorded by the source corpus.

Author(s): Hartshorne, Robin | Abstract: We extend the theory of generalized divisors so as to work on any scheme $X$ satisfying the condition $S_2$ of Serre. We define a generalized notion of Gorenstein biliaison for schemes in projective space. With this we give a new proof in a stronger form of the theorem of Gaeta, that standard determinantal schemes are in the Gorenstein biliaison class of a complete intersection. We also show, for schemes of codimension three in ${\mathbb P}^n$, that the relation of Gorenstein biliaison is equivalent to the relation of even strict Gorenstein liaison.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/585c128dadb9a71a7be1ce27cc1736f0d121bc89

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

ACM bundles on cubic surfaces (2008, background): “We say that two equidimensional subschemes Z1, Z2 of codimension 1 of Y without embedded components are strictly G-linked by a subscheme G ⊂ Y if G contains Z1 and Z2, JZi ,G ∼= Hom(OZj ,OG) for i, j = 1, 2, i 6= j , and there is an m ∈ Z such that G is linearly equivalent to mHY +MY where MY is the”
Gorenstein liaison and ACM sheaves (2003, unknown): “Definition 1.4. We recall the notion of biliaison from [15, 5.4.7], [3], [ 7 ], [9].”
F-adjunction (2009, background): “If one wishes to assume that R is not necessarily normal and that 1 = 0, or even that 1 is some sort of appropriate generalization of a Q-divisor (see for example [Hartshorne 2007] or [Kollár et al.”