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Mathematics, Algebraic Geometry
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.
