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Seminar

Fellowship of the Ring, National Seminar: When are multidegrees positive? April 29, 2021 (01:30 PM PDT - 03:00 PM PDT)
Parent Program: --
Location: MSRI: Online/Virtual
Speaker(s) Jonathan Montaño (New Mexico State University)
Description

To attend this seminar, you must register in advance, by clicking HERE.

Video

When are Multidegrees Positive

Abstract/Media

To attend this seminar, you must register in advance, by clicking HERE.

Multidegrees of multiprojective varieties extend the notion of degree of projective varieties. These invariants can be defined via intersection theory, or algebraically as the leading coefficients of multivariate Hilbert polynomials. It follows that multidegrees are nonnegative integers, so a fundamental question is: When are multidegrees positive?

In the first part of the talk, I will survey definitions and key properties of degrees and multidegrees, including some examples.

In the second part, I will present a complete characterization of the positivity of multidegrees, and establish a combinatorial description using convex geometry. I will also show applications of our result to mixed multiplicities of ideals and to the support of Schubert polynomials. The talk is based on joint work with F. Castillo, Y. Cid-Ruiz, B. Li, and N. Zhang.

Asset no preview Notes 1.93 MB application/pdf

When are Multidegrees Positive