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arXiv · 1901.06586

Segre indices and Welschinger weights as options for invariant count of real lines

Sergey Finashin·Viatcheslav Kharlamov
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Abstract

In our previous paper we have elaborated a certain signed count of real lines on real projective n-dimensional hypersurfaces of degree 2n-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 threefolds.

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Sergey Finashin, Viatcheslav Kharlamov. 2019-11-16. Segre indices and Welschinger weights as options for invariant count of real lines. https://doi.org/10.1093/imrn%2Frnz208

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