7 papers · 1 filter
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…
Hyperbolicity of varieties of log general type
Kenneth Ascher, Amos Turchet
These notes provide an overview of various notions of hyperbolicity for varieties of log general type from the viewpoint of both arithmetic and birational geometry. The main result…
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…
Hyperbolicity and uniformity of varieties of log general type
Kenneth Ascher, Kristin DeVleming, Amos Turchet
Projective varieties with ample cotangent bundle satisfy many notions of hyperbolicity, and one goal of this paper is to discuss generalizations to quasi-projective varieties. A ma…
Stable pair compactifications of the moduli space of degree one del pezzo surfaces via elliptic fibrations
Kenneth Ascher, Dori Bejleri
A degree one del Pezzo surface is the blowup of P^2 at 8 general points. By the classical Cayley-Bacharach Theorem, there is a unique 9th point whose blowup produces a rational ell…