6 papers
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…
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…