On the existence of a Gysin morphism for the Blow-up of an ordinary singularity

TL;DR

This paper characterizes when blow-up maps of ordinary singularities admit a natural Gysin morphism, providing conditions for the existence of a compatible bivariant class in algebraic geometry.

Contribution

It introduces criteria for the existence of a Gysin morphism in the context of blow-ups of ordinary singularities, extending the understanding of bivariant classes.

Findings

Identifies conditions for Gysin morphism existence

Provides a characterization for blow-ups of ordinary singularities

Enhances the theoretical framework of algebraic geometry

Abstract

In this paper we characterize the Blowing-up maps of ordinary singularities for which there exists a natural Gysin morphism, i.e. a bivariant class $\theta \in Hom_{D(Y)}(R\pi_*\mathbb Q_X, \mathbb Q_Y)$, compatible with pullback and with restriction to the complement of the singularity.