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

## TL;DR

This paper explores geometric interpretations of a signed count of real lines on hypersurfaces, generalizing Segre species and Welschinger weights to provide invariant counts that serve as lower bounds.

## Contribution

It introduces new geometric interpretations of the local contributions to the signed count, extending Segre and Welschinger concepts to broader classes of hypersurfaces.

## Key findings

- Provides invariant lower bounds for real lines on hypersurfaces.
- Generalizes Segre species for cubic surfaces.
- Extends Welschinger weights to quintic threefolds.

## 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.