On Genus 1 Gromov-Witten invariants of Fano complete intersections

TL;DR

This paper investigates genus 1 Gromov-Witten invariants of Fano complete intersections, providing reconstruction theorems and explicit computations, advancing understanding of enumerative geometry in these varieties.

Contribution

It introduces a reconstruction theorem for genus 1 invariants with ambient insertions and computes specific invariants for certain Fano complete intersections.

Findings

Reconstruction theorem for genus 1 invariants with ambient insertions

Explicit computation of genus 1 invariants with 1 marked point

Complete reconstruction for cubic hypersurfaces (dimension ≠ 4) and odd quadrics

Abstract

We study genus 1 Gromov-Witten invariants of Fano complete intersections in the projective spaces. Among other things, we show a reconstruction theorem for genus 1 invariants with only ambient insertions, and compute the genus 1 invariants with 1 marked point. For cubic hypersurfaces of dimension $\neq 4$ and odd dimensional intersections of two quadrics, we obtain a complete reconstruction theorem for genus 1 Gromov-Witten invariants.