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2016 Contractions of del Pezzo surfaces to $\mathbb P^2$ or $\mathbb P^1\times \mathbb P^1$
Jae-Hyouk Lee
Rocky Mountain J. Math. 46(4): 1263-1273 (2016). DOI: 10.1216/RMJ-2016-46-4-1263

Abstract

In this article, we consider $r-1$ disjoint lines given in a del~Pezzo surface $S_{r}$ and study how to determine if a contraction given by the lines produces a map to $S_{1}$ (one point blow up of $\mathbb {P}^{2}$) or $\mathbb {P}^{1}\times \mathbb {P}^{1}$ by checking only the configuration of lines. Here, we show that we can determine if the disjoint lines produce a contraction to $\mathbb {P}^{1}\times \mathbb {P}^{1}$ by combining a quartic rational divisor class to them. We also study the quartic rational divisor classes along the configuration of lines in del Pezzo surfaces.

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Jae-Hyouk Lee. "Contractions of del Pezzo surfaces to $\mathbb P^2$ or $\mathbb P^1\times \mathbb P^1$." Rocky Mountain J. Math. 46 (4) 1263 - 1273, 2016. https://doi.org/10.1216/RMJ-2016-46-4-1263

Information

Published: 2016
First available in Project Euclid: 19 October 2016

zbMATH: 1365.14016
MathSciNet: MR3563181
Digital Object Identifier: 10.1216/RMJ-2016-46-4-1263

Subjects:
Primary: 14E05, 14J26

Rights: Copyright © 2016 Rocky Mountain Mathematics Consortium

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Vol.46 • No. 4 • 2016
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