# The Hodge numbers of O'Grady 10 via Ng\^o strings

## TL;DR

This paper calculates the Hodge numbers of O'Grady 10, a hyper-Kähler manifold, using advanced techniques involving Ngô strings and modular Lagrangian fibrations to refine existing theorems.

## Contribution

It introduces a refined approach to determine Hodge numbers of O'Grady 10 through Ngô support theorem enhancements.

## Key findings

- Hodge numbers of O'Grady 10 are explicitly computed.
- Refinement of Ngô Support Theorem applied to hyper-Kähler manifolds.
- New connections established between Ngô strings and Hodge theory.

## Abstract

We determine the Hodge numbers of the hyper-K\"ahler manifold known as O'Grady 10 by studying some related modular Lagrangian fibrations by means of a refinement of the Ng\^o Support Theorem.