Elliptic Calabi-Yau threefolds over a del Pezzo surface
Simon Rose, Noriko Yui
TL;DR
This paper studies elliptic Calabi-Yau threefolds over del Pezzo surfaces, focusing on their geometric properties and invariants like Gromov-Witten and Gopakumar-Vafa, with implications for string theory and algebraic geometry.
Contribution
It introduces a class of elliptic Calabi-Yau threefolds over del Pezzo surfaces and analyzes their generating functions for key enumerative invariants.
Findings
Explicit formulas for Gromov-Witten invariants
Relationships between invariants and surface geometry
Insights into string compactifications
Abstract
We consider certain elliptic threefolds over the projective plane (more generally over certain rational surfaces) with a section in Weierstrass normal form. In particular, over a del Pezzo surface of degree 8, these elliptic threefolds are Calabi-Yau threefolds. We will discuss especially the generating functions of Gromov-Witten and Gopakumar-Vafa invariants.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Geometry and complex manifolds