Minitwistor spaces, Severi varieties, and Einstein-Weyl structure

Nobuhiro Honda, Fuminori Nakata

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

In this article, we show that the space of nodal rational curves, which is so called a Severi variety (of rational curves), on any non-singular projective surface is always equipped with a natural Einstein-Weyl structure, if the space is 3-dimensional. This is a generalization of the Einstein-Weyl structure on the space of smooth rational curves on a complex surface, given by Hitchin. As geometric objects naturally associated to Einstein-Weyl structure, we investigate null surfaces and geodesics on the Severi varieties. Also, we see that if the projective surface has an appropriate real structure, then the real locus of the Severi variety becomes a positive definite Einstein-Weyl manifold. Moreover, we construct various explicit examples of rational surfaces having 3-dimensional Severi varieties of rational curves.

Original languageEnglish
Pages (from-to)293-323
Number of pages31
JournalAnnals of Global Analysis and Geometry
Volume39
Issue number3
DOIs
Publication statusPublished - 2011 Mar

Keywords

  • Einstein-Weyl structure
  • Minitwistor space
  • Nodal rational curve
  • Penrose correspondence
  • Severi variety
  • Twistor space

ASJC Scopus subject areas

  • Analysis
  • Political Science and International Relations
  • Geometry and Topology

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