# Derived invariance of the numbers $h^{0,p}(X)$

## TL;DR

This paper proves that for derived equivalent smooth projective varieties over complex numbers, the dimensions of the spaces of global sections of their p-th canonical sheaves are equal, establishing an invariance property.

## Contribution

It demonstrates the derived invariance of the Hodge numbers $h^{0,p}$ for smooth projective varieties over complex numbers, a previously unknown result.

## Key findings

- $h^{0,p}(X)$ is invariant under derived equivalence.
- Derived equivalence preserves certain Hodge numbers.
- The result applies to all $p$ for smooth projective varieties.

## Abstract

Let $X_1$ and $X_2$ be derived equivalent smooth projective varieties over the field of complex numbers. We prove that the numbers $h^{0,p}(X_1)$ and $h^{0,p}(X_2)$ are equal for any $p$.

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Source: https://tomesphere.com/paper/1907.08721