On Hodge-Riemann Cohomology Classes

Julius Ross; Matei Toma

On Hodge-Riemann Cohomology Classes

Algebraic Geometry 2021-06-22 v1

Authors: Julius Ross , Matei Toma

Abstract

We prove that Schur classes of nef vector bundles are limits of classes that have a property analogous to the Hodge-Riemann bilinear relations. We give a number of applications, including (1) new log-concavity statements about characteristic classes of nef vector bundles (2) log-concavity statements about Schur and related polynomials (3) another proof that normalized Schur polynomials are Lorentzian.

Keywords

hodge-riemann bilinear relations schur classes nef vector bundles log-concavity characteristic classes lorentzian polynomials

Cite

@article{arxiv.2106.11285,
  title  = {On Hodge-Riemann Cohomology Classes},
  author = {Julius Ross and Matei Toma},
  journal= {arXiv preprint arXiv:2106.11285},
  year   = {2021}
}

Comments

23 pages, comments welcome

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