On the GHKS compactification of the moduli space of K3 surfaces of degree two
Klaus Hulek, Christian Lehn, Carsten Liese
TL;DR
This paper explores a toroidal compactification of the moduli space of degree 2 K3 surfaces, utilizing mirror symmetry and birational geometry to analyze the associated toric fan.
Contribution
It provides a detailed analysis of the toric fan in the context of the GHKS compactification, building on previous methods and connecting mirror symmetry with moduli space compactification.
Findings
Characterization of the toric fan structure
Application of Dolgachev's mirror symmetry formulation
Extension of previous methods to new compactification context
Abstract
We investigate a toroidal compactification of the moduli space of K3 surfaces of degree originating from the program formulated by Gross-Hacking-Keel-Siebert. This construction uses Dolgachev's formulation of mirror symmetry and the birational geometry of the mirror family. Our main result in an analysis of the toric fan. For this we use the methods developed by two of us in a previous paper.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Advanced Algebra and Geometry