Syzygies on abelian surfaces, construction of singular divisors, and Newton-Okounkov bodies

Syzygies on abelian surfaces, construction of singular divisors, and Newton-Okounkov bodies

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Alex Küronya , Goethe Universität Frankfurt am Main
Fine Hall 322

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 Kollár-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 surfaces building on earlier work of Lazarsfeld-Pareschi-Popa.