The Genus One Gromov-Witten Invariants of Calabi-Yau Complete Intersections
Alexandra Popa
TL;DR
This paper derives mirror formulas for genus 1 Gromov-Witten invariants of Calabi-Yau complete intersections and verifies BPS integrality predictions in low degrees across various dimensions.
Contribution
It extends algebraic methods for mirror formulas to Calabi-Yau complete intersections, broadening the scope beyond hypersurfaces.
Findings
Mirror formulas for genus 1 invariants are obtained.
BPS integrality predictions are confirmed in low degrees.
Results apply to multiple dimensions (3, 4, 5).
Abstract
We obtain mirror formulas for the genus 1 Gromov-Witten invariants of projective Calabi-Yau complete intersections. We follow the approach previously used for projective hypersurfaces by extending the scope of its algebraic results; there is little change in the geometric aspects. As an application, we check the genus 1 BPS integrality predictions in low degrees for all projective complete intersections of dimensions 3, 4, and 5.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric and Algebraic Topology · Commutative Algebra and Its Applications