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Moduli of double covers and degree one del Pezzo surfaces
Kenneth Ascher, Dori Bejleri
Given a degree one del Pezzo surface with canonical singularities, the linear series generated by twice the anti-canonical divisor exhibits the surface as the double cover of the q…
Wall crossing for K-moduli spaces of plane curves
Kenneth Ascher, Kristin DeVleming, Yuchen Liu
We construct proper good moduli spaces parametrizing K-polystable -Gorenstein smoothable log Fano pairs , where is a Fano variety and is a rational mul…
Compact moduli of elliptic K3 surfaces
Kenneth Ascher, Dori Bejleri
We construct various modular compactifications of the space of elliptic K3 surfaces using tools from the minimal model program, and explicitly describe the surfaces parametrized by…
The Erdős-Ulam problem, Lang's conjecture, and uniformity
Kenneth Ascher, Lucas Braune, Amos Turchet
A rational distance set is a subset of the plane such that the distance between any two points is a rational number. We show, assuming Lang's Conjecture, that the cardinalities of…