Liaison by quasi-Gorenstein ideals | Commutative Algebra Seminar in Beijing

Abstract

This is joint work with Matteo Varbaro. Liaison theory began to be studied as a subject (rather than simply as a tool) by Apéry and Gaeta in the 1940s. Since then, many mathematicians have furthered its exploration. In his paper published 1981, Schenzel considered Gorenstein liaison and showed that Gorenstein liaison preserves the (generalized) Cohen-Macaulayness. In this talk, we investigate some extensions of Schenzel’s results. More concretely, given that each Gorenstein ring is a Cohen-Macaulay quasi-Gorenstein ring, we gen- eralized Schenzel’s results to the positively graded quasi-Gorenstein case. Addi- tionally, we will discuss some applications of liaison by quasi-Gorenstein ideals. In particular, our main result, when applied to Stanley-Reisner rings, yields a version of the classical Lefschetz duality of algebraic topology.