On the spectral properties of the quantum cohomology of odd quadrics

Shifler, Ryan M.; Warman, Stephanie

doi:10.2140/involve.2023.16.27

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On the spectral properties of the quantum cohomology of odd quadrics

Ryan M. Shifler and Stephanie Warman

Vol. 16 (2023), No. 1, 27–34

DOI: 10.2140/involve.2023.16.27

Abstract

Let $H^{∙} (OG)$ be the quantum cohomology (specialized at $q = 1$ ) of the $(2 n - 1)$ -dimensional quadric $OG$ . We will calculate the characteristic polynomial of the linear operators induced by quantum multiplication in $H^{∙} (OG)$ and the Frobenius–Perron dimension. We also check that Galkin’s lower bound conjecture holds for $OG$ .

Keywords

quantum cohomology, Frobenius–Perron dimension, odd quadrics

Mathematical Subject Classification

Primary: 14N35

Secondary: 15B48, 14N15, 14M15

Milestones

Received: 2 June 2021

Revised: 10 February 2022

Accepted: 23 March 2022

Published: 14 April 2023

Communicated by Ravi Vakil

Authors

Ryan M. Shifler
Department of Mathematical Sciences Salisbury University Salisbury, MD United States

Stephanie Warman
Department of Mathematical Sciences Salisbury University Salisbury, MD United States

Vol. 16, No. 1, 2023