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

Date

2021-03-01

Author

Finashin, Sergey

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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.

URI

https://hdl.handle.net/11511/89920

Journal

INTERNATIONAL MATHEMATICS RESEARCH NOTICES

DOI

https://doi.org/10.1093/imrn/rnz208

Collections

Department of Mathematics, Article

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Citation Formats

S. Finashin, “Segre Indices and Welschinger Weights as Options for Invariant Count of Real Lines,” INTERNATIONAL MATHEMATICS RESEARCH NOTICES, pp. 4051–4078, 2021, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/89920.