Hodge-Riemann Classes and Schur Polynomials

Abstract: The classical Hodge-Riemann bilinear relations are statements about the intersection form associated to the self-wedge product of a K\"ahler form on a compact complex manifold. Gromov initiated the question as to whether there are other cohomology that give rise these same bilinear relations, and proved that this is the case for the intersection of (possibly different) K\"ahler classes. In this talk I will discuss joint work with Matei Toma in which we prove that the Schur classes of ample vector bundles have the Hodge-Riemann bilinear relations (at least on $H^{1,1}$). This gives rise to a number of new inequalities among characteristic classes of ample vector bundles that should be thought of as generalizations of the Khovanskii-Tessier inequalities. And if time allows I will also discuss how this extends to the non-projective case and beyond.

algebraic geometry

Audience: researchers in the topic

ZAG (Zoom Algebraic Geometry) seminar

Series comments: Description: ZAG seminar

The seminar takes place on Tuesdays and Thursdays via Zoom. Zoom passwords are given via mailing list on Fridays. To join the mailing list go to the website.

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Times vary to accommodate speakers time zones but times will be announced in GMT time.