Newton-Okounkov bodies and Picard numbers on surfaces

Julio José Moyano-Fernández, Matthias Nickel, Joaquim Roé

We study the shapes of all Newton-Okounkov bodies ${\Delta }_v(D)$ of a given big divisor $D$ on a surface $S$ with respect to all rank 2 valuations $v$ of $K(S)$. We obtain upper bounds…