6,678 research outputs found
ADE surfaces and their moduli
We define a class of surfaces corresponding to the ADE root lattices and
construct compactifications of their moduli spaces as quotients of projective
varieties for Coxeter fans, generalizing Losev-Manin spaces of curves. We
exhibit modular families over these moduli spaces, which extend to families of
stable pairs over the compactifications. One simple application is a geometric
compactification of the moduli of rational elliptic surfaces that is a finite
quotient of a projective toric variety.Comment: A streamlined and expanded versio
From Cracked Polytopes to Fano Threefolds
We construct Fano threefolds with very ample anti-canonical bundle and Picard
rank greater than one from cracked polytopes - polytopes whose intersection
with a complete fan forms a set of unimodular polytopes - using Laurent
inversion; a method developed jointly with Coates-Kasprzyk. We also give
constructions of rank one Fano threefolds from cracked polytopes, following
work of Christophersen-Ilten and Galkin. We explore the problem of classifying
polytopes cracked along a given fan in three dimensions, and classify the
unimodular polytopes which can occur as 'pieces' of a cracked polytope.Comment: New introduction and section on the connection with the Gross-Siebert
program. 46 page
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