Nef and semiample divisors on rational surfaces
Antonio Laface, Damiano Testa
TL;DR
This paper characterizes when nef divisors on rational surfaces with pseudo-effective anticanonical divisors are semiample, providing a criterion applicable over any characteristic and exploring implications for Mori dream surfaces.
Contribution
It offers a necessary and sufficient condition for nef divisors to be semiample on certain rational surfaces, extending understanding across different characteristics.
Findings
Criterion for semi-ampleness of nef divisors
Application to Mori dream surfaces in complex case
Characterization valid over any characteristic
Abstract
In this paper we study smooth projective rational surfaces, defined over an algebraically closed field of any characteristic, with pseudo-effective anticanonical divisor. We provide a necessary and sufficient condition in order for any nef divisor to be semiample. We adopt our criterion to investigate Mori dream surfaces in the complex case.
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