中央研究院數學研究所

Seminar in Algebra

Betti Numbers of Monomial Surfaces and Their Projective Closures

2026/05/08 (Fri.) 14:00~15:00

Date : 2026/05/08 (Fri.) 14:00~15:00
Location : Seminar Room 617, Institute of Mathematics (NTU Campus)
Speaker : Kuei-Nuan Lin (Penn State University)
Organizer : Julie Tzu-Yueh Wang (AS)
Abstract :
In this talk, I will discuss when the Betti sequences of an affine semigroup ring agree with those of its projective closure.
Using Gröbner basis methods, we characterize when a projective monomial hypersurface is arithmetically Cohen--Macaulay and show that this condition ensures the equality of affine and projective Betti sequences.
We further interpret this homological invariance in terms of Apéry sets, extending results known for monomial curves to higher-dimensional semigroup rings. Finally, we give necessary and sufficient conditions for Gorensteinness.