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Geometric aspects of Newton–Okounkov bodies

Volume 116 / 2018

Alex Küronya, Victor Lozovanu Banach Center Publications 116 (2018), 137-212 MSC: 14C20, 14J99, 32Q15, 13F30. DOI: 10.4064/bc116-7

Abstract

This is a survey article on Newton–Okounkov bodies in projective geometry focusing on the relationship between positivity of divisors and Newton–Okounkov bodies. We build up the theory in the context of positive line bundles and devote time to study the special case of surfaces. The final part of the paper treats the application of constructing singular divisors and studying syzygies on abelian surfaces.

Authors

  • Alex KüronyaJohann-Wolfgang-Goethe Universität Frankfurt
    Institut für Mathematik
    Robert-Mayer-Straße 6-10
    D-60325 Frankfurt am Main, Germany
    and
    Budapest University of Technology and Economics
    Department of Algebra
    Egry József u. 1
    H-1111 Budapest, Hungary
    e-mail
  • Victor LozovanuLeibniz-Universität Hannover
    Institut für Algebraische Geometrie
    Welfengarten 1
    D-30167 Hannover, Germany
    e-mail

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