Siva Somasundaram

Purdue University

Gorenstein linkage of Ideals

A central open problem in Gorenstein liaison theory asks whether every Cohen–Macaulay ideal in a regular ring belongs to the Gorenstein linkage class of a complete intersection (is glicci). While the problem remains open in general, many positive results are known. I will present my proof that zero-dimensional ideals ($\mathfrak{m}$-primary) in a Gorenstein ring are glicci, and monomial ideals of height 3 in 4 dimensional polynomial ring is Glicci. Providing further evidence for the conjecture and, in particular, establishing it in dimension three over regular rings.