Vari\'et\'es projectives complexes dont l'\'eclat\'ee en un point est de Fano

TL;DR

This paper classifies complex projective manifolds whose blow-up at a point results in a Fano manifold, providing a complete characterization of such geometric structures.

Contribution

It offers a classification of complex projective manifolds with a point whose blow-up yields a Fano manifold, a novel result in algebraic geometry.

Findings

Identifies all manifolds with this property

Provides explicit classification results

Enhances understanding of blow-up and Fano conditions

Abstract

We classify complex projective manifolds $X$ for which there exists a point $a$ such that the blow-up of $X$ at $a$ is Fano.