Home /  COMA Colloquium: "Singularities of ideals admitting a squarefree Gröbner degeneration"

Seminar

COMA Colloquium: "Singularities of ideals admitting a squarefree Gröbner degeneration" May 15, 2024 (02:00 PM PDT - 03:00 PM PDT)
Parent Program:
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Speaker(s) Matteo Varbaro (Università di Genova)
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Keywords and Mathematics Subject Classification (MSC)
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Video

Singularities of ideals admitting a squarefree Gröbner degeneration

Abstract/Media

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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. In 2018, with Conca we raised the

question whether, in this situation, X being smooth implies that S/I is Cohen-Macaulay with negative

a-invariant (equivalently, S/I is a F-rational singularity). In 2019, in a joint paper with Constantinescu

and De Negri, we gave a positive answer to the question in some cases, and we turned the question into

a conjecture. However, it is still widely open, even when X is a curve. In this case, rephrasing it the conjecture

says that, 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 conjecture, giving

some evidence for it and explaining why it is difficult to show it in general. We will also discuss some recent

developments done in an ongoing work with Huang, Tarasova, and Witt.

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Singularities of ideals admitting a squarefree Gröbner degeneration