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Square-free Groebner degenerations

Banff International Research Station for Mathematical Innovation and Discovery

Let S be a polynomial ring, I a homogeneous ideal and denote by in(I) the initial ideal of I w.r.t. some term order on S. It is well-known that depth(S/I) >= depth(S/in(I)) and reg(S/I) <= reg(S/in(I)), and it is easy to produce examples for which these inequalities are strict. On the other hand, in generic coordinates equalities hold for a degrevlex term order, by a celebrated result of Bayer and Stillman. In a joint paper with Aldo Conca, we prove that the equalities hold as well under the assumption that in(I) is a square-free monomial ideal (for any term order), solving a conjecture of Herzog. In this talk, after discussing where this conjecture came from, I will sketch the proof of its solution.

Mathematics; Commutative rings and algebras; Algebraic geometry; Algebraic structures

video/mp4

Author affiliation: University of Genova

2019-03-23

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/69104

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/