Duke Mathematical Journal
- Duke Math. J.
- Volume 162, Number 10 (2013), 1877-1894.
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 with a surjective nonisomorphic endomorphism has bounded negativity (i.e., that is bounded below for prime divisors on ). 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.
Duke Math. J., Volume 162, Number 10 (2013), 1877-1894.
First available in Project Euclid: 11 July 2013
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Bauer, Thomas; Harbourne, Brian; Knutsen, Andreas Leopold; Küronya, Alex; Müller-Stach, Stefan; Roulleau, Xavier; Szemberg, Tomasz. Negative curves on algebraic surfaces. Duke Math. J. 162 (2013), no. 10, 1877--1894. doi:10.1215/00127094-2335368. https://projecteuclid.org/euclid.dmj/1373546606