Year: 2016
Type: preprint
Abstract: Let $(S,\mathcal L)$ be a smooth, irreducible, projective, complex surface, polarized by a very ample line bundle $\mathcal L$ of degree $d > 35$. In this paper we prove that $K^2_S\geq -d(d-6)$. The bound is sharp, and $K^2_S=-d(d-6)$ if and only if $d$ is even, the linear system $|H^0(S,\mathcal L)|$ embeds $S$ in a smooth rational normal scroll $T\subset \mathbb P^5$ of dimension $3$, and here, as a divisor, $S$ is linearly equivalent to $\frac{d}{2}Q$, where $Q$ is a quadric on $T$.
Source: arXiv (Cornell University)
Authors: Di Gennaro, Vincenzo, Franco, Davide
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2951406144