Strictly nef divisors and some remarks on a conjecture of Serrano

Abstract

Serrrano's Conjecture says that if $L$ is a strictly nef line bundle on a smooth projective variety $X$, then $K_X+tL$ is ample for $t>dimX+1$. In this paper I will prove a few cases of this conjecture. I will also prove a generalized version of this conjecture (due to Campana, Chen and Peternell) for surfaces. In the last section, assuming the SHGH conjecture, I will give a series of examples of strictly nef non ample divisors on surfaces of arbitary Kodaira dimension.

16 pages. Comments welcome

References in corpus (1)

• On Generalised Abundance, I

Cited by in corpus (1)

• Strictly nef vector bundles and characterizations of ${\mathbb{P}}^n$