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Journal Article

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

MPS-Authors
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Finashin,  Sergey
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons235068

Kharlamov,  Viatcheslav
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.1093/imrn/rnz208
(Publisher version)

https://doi.org/10.48550/arXiv.1901.06586
(Preprint)

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Citation

Finashin, S., & Kharlamov, V. (2021). Segre indices and Welschinger weights as options for invariant count of real lines. International Mathematics Research Notices, 2021(6), 4051-4078. doi:10.1093/imrn/rnz208.


Cite as: https://hdl.handle.net/21.11116/0000-0006-9DD9-5
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.