Newton--Okounkov bodies of curve classes

Lucie Devey (1, 2)

1 IF - Institut Fourier
2 Goethe-Universität Frankfurt am Main

The purpose of the paper is to initiate the development of the theory of Newton Okounkov bodies of curve classes. Our denition is based on making a fundamental property of NewtonOkounkov bodies hold also in the curve case: the volume of the NewtonOkounkov body of a curve is a volume-type function of the original curve. This construction allows us to conjecture a new relation between NewtonOkounkov bodies, we prove it in certain cases.

Domaines: Géométrie algébrique [math.AG]; Géométrie métrique [math.MG]; Variables complexes [math.CV]

Lucie Devey. Newton--Okounkov bodies of curve classes. 2022. ⟨hal-03786725⟩