Enumerative geometry of $K3$ surfaces
Thomas Dedieu
TL;DR
This paper reviews key enumerative geometry results related to K3 surfaces, highlighting their connections to conjectures and recent mathematical advances without relying on Gromov-Witten theory.
Contribution
It compiles and explains various enumerative results about K3 surfaces, clarifying their proofs and implications in a comprehensive manner.
Findings
Confirmation of Yau--Zaslow conjecture
Validation of G"ottsche and Katz--Klemm--Vafa conjectures
Summary of results by Beauville, Bryan, Leung, Pandharipande, Maulik, Thomas
Abstract
The aim of these notes is to explain various enumerative results about surfaces without assuming familiarity with Gromov--Witten theory. The enumerative results in question are due to Beauville, Bryan and Leung, Pandharipande, Maulik, Thomas, and others, and confirm conjectures made by Yau--Zaslow, G\"ottsche, and Katz--Klemm--Vafa.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric and Algebraic Topology · Computational Geometry and Mesh Generation