Topology Atlas | Conferences


Knots in Washington XLVI: 70th Birthday of Oleg Viro;
May 4-6, 2018
George Washington University,
Washington, DC, USA

Organizers
Valentina Harizanov (GWU), Jozef H. Przytycki (GWU), Yongwu Rong (GWU), Radmila Sazdanovic (NCSU), Alexander Shumakovitch (GWU)

Conference Homepage


Little variations on the theme of counting real lines.
by
Viatcheslav Kharlamov
Strasbourg University

As it was observed a few years ago, there exists a certain signed count of real lines on real projective hypersurfaces of degree 2n+1 and dimension n that, contrary to the honest "cardinal" count, is independent of the choice of a hypersurface, and by this reason provides, as a consequence, a strong lower bound on the honest count. In this invariant signed count the input of a line is given by its local contribution to the Euler number of a certain auxiliary universal vector bundle.

The aim of the talk is to present other, in a sense more geometric, interpretations of the signs involved in the invariant count. In particular, this provides some generalizations of Segre indices of real lines on cubic surfaces and Welschinger weights of real lines on quintic threefolds.

This is a joint work with S.Finashin.

Date received: April 22, 2018


Copyright © 2018 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cboy-26.