Moduli of Gorenstein Q-homology projective planes
Matthias Schuett

TL;DR
This paper classifies all complex Q-homology projective planes with certain singularities and trivial canonical bundle, describing their moduli spaces explicitly as rational curves over Q.
Contribution
It provides a complete classification of these surfaces, detailing their one-dimensional moduli spaces and explicit constructions via elliptic surfaces and involutions.
Findings
31 types of such surfaces identified
All moduli are rational curves over Q
Explicit families constructed using elliptic surfaces
Abstract
We give a complete classification of complex Q-homology projective planes with isolated rational double point singularities and numerically trivial canonical bundle. There are 31 types, and each has one-dimensional moduli. In fact, all moduli curves are rational and defined over Q, and we determine all families explicitly using extremal rational elliptic surfaces and Enriques involutions of base change type.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Algebraic structures and combinatorial models
