Negative curves on algebraic surfaces

We study curves of negative self-intersection on algebraic surfaces. In contrast to what occurs in positive characteristics, it turns out that any smooth complex projective surface X with a surjective nonisomorphic endomorphism has bounded negativity (i.e., that C^{2} is bounded below for prime divi...

Full description

Saved in:
Bibliographic Details
Published in:Duke mathematical journal 2013-07, Vol.162 (10), p.1877-1894
Main Authors: Bauer, Thomas, Harbourne, Brian, Knutsen, Andreas Leopold, Küronya, Alex, Müller-Stach, Stefan, Roulleau, Xavier, Szemberg, Tomasz
Format: Article
Language:English
Subjects:
14C17
14G35
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We study curves of negative self-intersection on algebraic surfaces. In contrast to what occurs in positive characteristics, it turns out that any smooth complex projective surface X with a surjective nonisomorphic endomorphism has bounded negativity (i.e., that C^{2} is bounded below for prime divisors C on X ). We prove the same statement for Shimura curves on quaternionic Shimura surfaces of Hilbert modular type. As a byproduct, we obtain that there exist only finitely many smooth Shimura curves on such a surface. We also show that any set of curves of bounded genus on a smooth complex projective surface must have bounded negativity.
ISSN:0012-7094
1547-7398
DOI:10.1215/00127094-2335368