Back to Commutative Algebra Seminar: Fall 2025
Commutative Algebra Seminar
Date: Friday, Nov 21, 2025
Time: 2:00PM - 3:00PM
Location: LCB 222
Yairon Cid-Ruiz
North Carolina State University
Title |
Mixed Segre zeta functions and their log-concavity |
Abstract |
In this talk, we introduce the mixed Segre zeta function associated with a sequence of homogeneous ideals in a polynomial ring. This power series encodes information about the mixed Segre classes that arise when the ideals are extended to projective spaces of arbitrarily large dimension. Our construction generalizes and unifies classical results by Kleiman and Thorup on mixed Segre classes and by Aluffi on Segre zeta functions. We show that this function is always rational, with poles determined by the degrees of the generators of the ideals, and that it depends only on the integral closures of these ideals. Finally, we explain how the numerator of a modified form of the mixed Segre zeta function exhibits a remarkable combinatorial property: its homogenization is denormalized Lorentzian in the sense of Brändén and Huh. |
Commutative Algebra