Higher genus Gromov-Witten invariants of the Grassmannian, and the Pfaffian Calabi-Yau threefolds

TL;DR

This paper computes higher genus Gromov-Witten invariants for certain Calabi-Yau threefolds derived from Grassmannian and Pfaffian varieties by solving the BCOV holomorphic anomaly equation, extending previous enumerative geometry results.

Contribution

It provides explicit calculations of higher genus invariants for Calabi-Yau threefolds in Grassmannian and Pfaffian settings, using the BCOV anomaly equation, a novel approach for these geometries.

Findings

Higher genus invariants up to genus 5 are determined.

The invariants are computed for Calabi-Yau threefolds in Grassmannian and Pfaffian varieties.

The results extend the understanding of enumerative geometry in derived equivalent Calabi-Yau manifolds.

Abstract

We solve Bershadsky-Cecotti-Ooguri-Vafa (BCOV) holomorphic anomaly equation to determine the higher genus Gromov-Witten invariants ($g \leq 5$) of the derived equivalent Calabi-Yau threefolds, which are of the appropriate codimensions in the Grassmannian Gr(2,7) and the Pfaffian Pf(7).