Rocky Mountain Journal of Mathematics

Contractions of del Pezzo surfaces to $\mathbb P^2$ or $\mathbb P^1\times \mathbb P^1$

Jae-Hyouk Lee

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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.

Article information

Source
Rocky Mountain J. Math., Volume 46, Number 4 (2016), 1263-1273.

Dates
First available in Project Euclid: 19 October 2016

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1476884582

Digital Object Identifier
doi:10.1216/RMJ-2016-46-4-1263

Mathematical Reviews number (MathSciNet)
MR3563181

Zentralblatt MATH identifier
1365.14016

Subjects
Primary: 14E05: Rational and birational maps 14J26: Rational and ruled surfaces

Keywords
del Pezzo surface Gosset polytopes Weyl action

Citation

Lee, Jae-Hyouk. Contractions of del Pezzo surfaces to $\mathbb P^2$ or $\mathbb P^1\times \mathbb P^1$. Rocky Mountain J. Math. 46 (2016), no. 4, 1263--1273. doi:10.1216/RMJ-2016-46-4-1263. https://projecteuclid.org/euclid.rmjm/1476884582


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References

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