# Rational differential forms on the variety of flexes of plane cubics

## TL;DR

This paper proves that for any positive integer d, the variety of flexes of plane cubics admits no nonzero regular differential d-forms, revealing a specific geometric property of these varieties.

## Contribution

It establishes the nonexistence of nonzero regular differential forms of any positive degree on the variety of flexes of plane cubics, a new result in algebraic geometry.

## Key findings

- No nonzero regular differential d-forms exist for any positive integer d.
- The result applies to all smooth irreducible projective varieties birationally equivalent to the variety of flexes.
- This enhances understanding of the geometric structure of the variety of flexes of plane cubics.

## Abstract

We prove that for every positive integer $d$, there are no nonzero regular differential $d$-forms on every smooth irreducible projective algebraic variety birationally isomorphic to the variety of flexes of plane cubics.