Existence of a singular projective variety with an arbitrary set of characteristic numbers

TL;DR

This paper demonstrates that for singular projective varieties, it is possible to realize any set of characteristic numbers, extending the known limitations for smooth compact complex manifolds.

Contribution

The authors prove the existence of singular projective varieties with arbitrary characteristic numbers, showing no divisibility restrictions apply in the singular case.

Findings

Existence of singular projective varieties with any characteristic numbers

Extension of characteristic number realizability to singular varieties

No divisibility constraints for singular varieties' characteristic numbers

Abstract

It is known that Chern characteristic numbers of compact complex manifolds cannot have arbitrary values. They satisfy certain divisability conditions. W. Ebeling and S. M. Gusein-Zade gave a definition of Chern characteristic numbers of singular compact complex analytic varieties. We prove that there exists a singular projective variety with an arbitrary set of characteristic numbers.