20 citations · 61 across the 20 of their papers we have counts for
25 papers
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…
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…
Moduli of boundary polarized Calabi-Yau pairs
Kenneth Ascher, Dori Bejleri, Harold Blum +4
We develop the moduli theory of boundary polarized CY pairs, which are slc Calabi-Yau pairs such that is ample. The motivation for studying this moduli problem is to co…
Wall crossing for moduli of stable log pairs
Kenneth Ascher, Dori Bejleri, Giovanni Inchiostro +1
We prove, under suitable conditions, that there exist wall-crossing and reduction morphisms for moduli spaces of stable log pairs in all dimensions as one varies the coefficients o…
K-stability and birational models of moduli of quartic K3 surfaces
Kenneth Ascher, Kristin DeVleming, Yuchen Liu
We show that the K-moduli spaces of log Fano pairs where is a quartic surface interpolate between the GIT moduli space of quartic surfaces and the Baily-Bo…
Smoothability of relative stable maps to stacky curves
Kenneth Ascher, Dori Bejleri
Using log geometry, we study smoothability of genus zero twisted stable maps to stacky curves relative to a collection of marked points. One application is to smoothing semi-log ca…
K-moduli of curves on a quadric surface and K3 surfaces
Kenneth Ascher, Kristin DeVleming, Yuchen Liu
We show that the K-moduli spaces of log Fano pairs where is a -curve and their wall crossings coincide with the VGIT quotients of…
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…
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…
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…
Enumerating Hassett's wall and chamber decomposition of the moduli space of weighted stable curves
Kenneth Ascher, Connor Dubé, Daniel Gershenson +1
Hassett constructed a class of modular compactifications of the moduli space of pointed curves by adding weights to the marked points. This leads to a natural wall and chamber deco…
Moduli of weighted stable elliptic surfaces and invariance of log plurigenera
Kenneth Ascher, Dori Bejleri, Giovanni Inchiostro
This is the third paper in a series of work on weighted stable elliptic surfaces - elliptic fibrations with section and marked fibers weighted between zero and one. Motivated by Ha…
Moduli of fibered surface pairs from twisted stable maps
Kenneth Ascher, Dori Bejleri
We use the theory of twisted stable maps to Deligne-Mumford stacks to construct compactifications of the moduli space of pairs where is a fibered surfa…
Log canonical models of elliptic surfaces
Kenneth Ascher, Dori Bejleri
We give a classification of the log canonical models of elliptic surface pairs consisting of an elliptic fibration, a section, and a weighted sum of marked fibers. In particular, w…
Bounding heights uniformly in families of hyperbolic varieties
Kenneth Ascher, Ariyan Javanpeykar
We show that, assuming Vojta's height conjecture, the height of a rational point on an algebraically hyperbolic variety can be bounded "uniformly" in families. This generalizes a r…
A Generic Slice of the Moduli Space of Line Arrangements
Kenneth Ascher, Patricio Gallardo
We study the compactification of the locus parametrizing lines with a fixed intersection to a given line, inside the moduli space of line arrangements in the projective plane const…
A fibered power theorem for pairs of log general type
Kenneth Ascher, Amos Turchet
Let be a stably family with log canonical general fiber. We prove that, after a birational modification of the base , there is a morphism from a h…
Rational points on twisted K3 surfaces and derived equivalences
Kenneth Ascher, Krishna Dasaratha, Alexander Perry +1
Using a construction of Hassett--Várilly-Alvarado, we produce derived equivalent twisted K3 surfaces over , , and , where one has a rational p…