Contractions of del Pezzo surfaces to ℙ2 OR ℙ1 x ℙ1

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Abstract

In this article, we consider r - 1 disjoint lines given in a del Pezzo surface Sr and study how to determine if a contraction given by the lines produces a map to S1 (one point blow up of ℙ2) or ℙ1 x ℙ1 by checking only the configuration of lines. Here, we show that we can determine if the disjoint lines produce a contraction to ℙ1 x ℙ1 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.

Original languageEnglish
Pages (from-to)1263-1273
Number of pages11
JournalRocky Mountain Journal of Mathematics
Volume46
Issue number4
DOIs
StatePublished - 2016

Keywords

  • Del Pezzo surface
  • Gosset polytopes
  • Weyl action

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