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Boundedness results for families of non-canonically polarized projective varieties
Kenneth Ascher, Behrouz Taji
We prove that, over a smooth quasi-projective curve, the set of non-isotrivial, smooth and projective families of polarized varieties with a fixed Hilbert polynomial and semi-ample…
Chow and cohomology rings of moduli stacks of plane quartics
Kenneth Ascher, Donggun Lee
This paper studies the Chow and cohomology rings of the Hacking moduli stack of plane quartics. We construct a smooth proper Deligne--Mumford stack resol…
Hassett--Keel Program in genus four
Kenneth Ascher, Kristin DeVleming, Yuchen Liu +1
The Hassett--Keel program seeks to give a modular interpretation to the steps of the log minimal model program of . The goal of this paper is to complete…
The algebraic Green-Griffiths-Lang conjecture for complements of very general pairs of divisors
Kenneth Ascher, Amos Turchet, Wern Yeong
We prove that the complement of a very general pair of hypersurfaces of total degree in is algebraically hyperbolic modulo a proper closed subvariety. This prov…
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…