Geometric aspects of Newton–Okounkov bodies
Volume 116 / 2018
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.
