Liaison Addition and the Structure of a Gorenstein Liaison Class
نویسنده
چکیده
We study the concept of liaison addition for codimension two subschemes of an arithmetically Gorenstein projective scheme. We show how it relates to liaison and biliaison classes of subschemes and use it to investigate the structure of Gorenstein liaison equivalence classes, extending the known theory for complete intersection liaison of codimension two subschemes. In particular, we show that on the non-singular quadric threefold in projective 4-space, every non-licci ACM curve can be obtained from a single line by successive liaison additions with lines and CI-biliaisons.
منابع مشابه
Liaison Classes of Modules
We propose a concept of module liaison that extends Gorenstein liaison of ideals and provides an equivalence relation among unmixed modules over a commutative Gorenstein ring. Analyzing the resulting equivalence classes we show that several results known for Gorenstein liaison are still true in the more general case of module liaison. In particular, we construct two maps from the set of even li...
متن کاملA SHORT PROOF OF A RESULT OF NAGEL
Let $(R,fm)$ be a Gorenstein local ring and$M,N$ be two finitely generated modules over $R$. Nagel proved that if $M$ and $N$ are inthe same even liaison class, thenone has $H^i_{fm}(M)cong H^i_{fm}(N)$ for all $iIn this paper, we provide a short proof to this result.
متن کاملExperiments with Gorenstein Liaison
We give some experimental data of Gorenstein liaison, working with points in P and curves in P , to see how far the familiar situation of liaison, biliaison, and Rao modules of curves in P will extend to subvarieties of codimension 3 in higher P . AMS classification numbers: 14H50, 14M07
متن کاملGorenstein Liaison of curves in P
Let k be an algebraically closed field of characteristic zero, S = k[X0, X1, X2, X3, X4] and P = Proj(S). By a curve we always mean a closed one-dimensional subscheme of P which is locally Cohen-Macaulay and equidimensional. The main purpose of this paper is to show that arithmetically Cohen-Macaulay curves C ⊂ P lying on a “general” arithmetically Cohen-Macaulay surface X ⊂ P with degree matri...
متن کاملSome Examples of Gorenstein Liaison in Codimension Three
Gorenstein liaison seems to be the natural notion to generalize to higher codimension the well-known results about liaison o varieties of codimension 2 in projective space. In this paper we study points in P and cuves in P in an attempt to see how far typical codimension 2 results will extend. While the results are satisfactory for small degree, we find in each case examples where we cannot dec...
متن کامل