Varieties with two smooth blow up structures

TL;DR

This paper classifies certain smooth projective varieties with two distinct blow-up structures, providing insights into quadro-cubic Cremona transformations.

Contribution

It offers a classification of Picard rank 2 varieties with dual blow-up structures, linking them to specific Cremona transformations.

Findings

Classified varieties with two blow-up structures of different dimensions.

Characterized the quadro-cubic Cremona transformation.

Provided geometric conditions for these varieties.

Abstract

We classify smooth projective varieties of Picard rank 2 which has two structures of blow-up of projective space along smooth subvarieties of different dimensions. This gives a characterization of the so called quadro-cubic Cremona transformation.