Classifies boundary surfaces in the KSBA-moduli space of elliptic surfaces with bisections, recovers moduli stack results for elliptic surfaces with sections via new proofs avoiding specific MMP steps, and compactifies the moduli stack of hyperelliptic K3 surfaces.
Explicit stable models of elliptic surfaces with sections
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abstract
In this note we show how to find the stable model of a one-parameter family of elliptic surfaces with sections. More specifically, we perform the log Minimal Model Program in an explicit manner by means of toric geometry, in each such one parameter family. This way we obtain an explicit combinatorial description of the surfaces that may occur at the boundary of moduli (as well as a new proof of the completeness of the moduli space)
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Moduli of surfaces fibered in (log) Calabi-Yau pairs II: elliptic surfaces
Classifies boundary surfaces in the KSBA-moduli space of elliptic surfaces with bisections, recovers moduli stack results for elliptic surfaces with sections via new proofs avoiding specific MMP steps, and compactifies the moduli stack of hyperelliptic K3 surfaces.