11 citations · 15 across the 5 of their papers we have counts for
7 papers · 1 filter
On the existence of flips
Christopher Hacon, James McKernan
We prove the existence of flips in dimension n, contingent on the termination of real flips in dimension n-1.
Shokurov's Rational Connectedness Conjecture
Christopher D Hacon, James McKernan
We prove a conjecture of V. V. Shokurov which in particular implies that the fibers of a resolution of a variety with divisorial log terminal singularities are rationally chain con…
Singularities of divisors of low degree on abelian varieties
Olivier Debarre, Christopher Hacon
Building on previous work of Kollar, Ein, Lazarsfeld, and Hacon, we show that ample divisors of low degree on an abelian variety have mild singularities in case the abelian variety…
Holomorphic one-forms on varieties of general type
Christopher D. Hacon, Sándor J. Kovács
It has been conjectured that varieties of general type do not admit nowhere vanishing holomorphic one-forms. We confirm this conjecture for smooth minimal varieties and for varieti…
Birational characterization of products of curves of genus 2
Christopher D. Hacon, Rita Pardini
Let X be a variety of maximal Albanese dimension. In this paper we prove that if χ(ω_X)=1 then the q(X)<=2dim X and if q(X)=2dim X, then X is birational to a product of curves of g…
A derived category approach to generic vanishing
Christopher D. Hacon
We prove a Generic Vanishing Theorem for coherent sheaves on an abelian variety over an algebraically closed field . When $k=\CC$ this implies a conjecture of Green and Lazarsfe…