Events for 01/31/2025 from all calendars

Departmental Colloquia

Time: 4:00PM - 5:00PM

Location: Bloc 117

Speaker: Ionut Chifan

Title: Ionut Chifan

Geometry Seminar

Time: 5:00PM - 6:00PM

Location: BLOC 302

Speaker: M. Varbaro

Title: Singularities of varieties with a squarefree Gröbner degeneration

Abstract: Let S be a polynomial ring over a field, I a homogeneous ideal, X the projective variety defined by I, and < a monomial order on S. Assume that in_<(I) is squarefree. When < is the revlex order, the smoothness of X forces S/I to be Cohen-Macaulay with negative a-invariant (hence a (F)-rational singularity). We will discuss on the problem wether this phenomenon can happen in general; this is not clear even when X is a curve and < is lex. In  this case, rephrasing the question it asks: if X is a smooth projective curve admitting some embedding for which the defining ideal has a squarefree initial ideal, then X must have genus 0. In this talk we will largely discuss this problem, giving some evidence for it and explaining why it is difficult to show it in general.