Flexibility of affine cones over a smooth complete intersection of two quadrics

TL;DR

This paper proves the flexibility of certain affine varieties, specifically the complements of quadrics in projective space and affine cones over smooth complete intersections of two quadrics, expanding understanding of their geometric properties.

Contribution

It establishes the flexibility of affine cones over smooth complete intersections of two quadrics, a new result in the study of affine algebraic varieties.

Findings

Affine cones over smooth complete intersections of two quadrics are flexible.

Complement of a projective quadric of rank at least three in projective space is flexible.

The results extend the class of known flexible affine varieties.

Abstract

We prove flexibility of two families of affine varieties: the complement in $\mathbb{P}^n$ of a projective quadric of rank at least three and affine cones over a smooth complete intersection of two quadrics in $\mathbb{P}^{n + 2}$, $n \ge 3$.