Simple connectedness of Fano log pairs with semi-log canonical singularities

TL;DR

This paper proves that unions of semi-log canonical strata in Fano log pairs are simply connected, confirming a conjecture and providing new insights into the topological properties of these algebraic structures.

Contribution

It establishes the simple connectedness of Fano log pairs with semi-log canonical singularities, confirming a conjecture and advancing understanding of their topological features.

Findings

Unions of slc strata in Fano log pairs are simply connected

Fano log pairs with semi-log canonical singularities are simply connected

Confirms a conjecture of the first author

Abstract

We show that any union of slc strata of a Fano log pair with semi-log canonical singularities is simply connected. In particular, Fano log pairs with semi-log canonical singularities are simply connected, which confirms a conjecture of the first author.