Alex Kuronya

Title: Construction of singular divisors, Newton-Okounkov bodies, and syzygies on abelian varieties

Abstract: Constructing divisors with prescribed singularities is one of the most powerful techniques 
in modern projective geometry, leading to proofs of major results in the minimal model program
and the strongest general positivity theorems by Angehrn-Siu and Kollar-Matsusaka. 
We present a novel method for constructing singular divisors on surfaces based on infinitesimal 
Newton-Okounkov bodies. As an application of our machinery we discuss a Reider-type theorem for 
higher syzygies on abelian varieties building on earlier work of Lazarsfeld-Pareschi-Popa.