Segre Indices and Welschinger Weights as Options for Invariant Count of Real Lines


FİNASHİN S. , Kharlamov V.

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, vol.2021, no.6, pp.4051-4078, 2021 (Journal Indexed in SCI) identifier

  • Publication Type: Article / Article
  • Volume: 2021 Issue: 6
  • Publication Date: 2021
  • Doi Number: 10.1093/imrn/rnz208
  • Title of Journal : INTERNATIONAL MATHEMATICS RESEARCH NOTICES
  • Page Numbers: pp.4051-4078

Abstract

In our previous paper [5] we have elaborated a certain signed count of real lines on real hypersurfaces of degree 2n - 1 in Pn+1. Contrary to the honest "cardinal" count, it is independent of the choice of a hypersurface and, by this reason, provides a strong lower bound on the honest count. In this count the contribution of a line is its local input to the Euler number of a certain auxiliary vector bundle. The aim of this paper is to present other, in a sense more geometric, interpretations of this local input. One of them results from a generalization of Segre species of real lines on cubic surfaces and another from a generalization of Welschinger weights of real lines on quintic three-folds.