Hodge theory, algebraic cycles of hyper-K\"ahler manifolds

TL;DR

This thesis investigates algebraic cycles in hyper-K"ahler and Calabi-Yau manifolds, aiming to understand conjectures about their Chow rings and birational invariants.

Contribution

It advances the understanding of Beauville's and Voisin's conjectures on Chow rings and explores birational invariants of hyper-K"ahler manifolds.

Findings

Progress on Beauville's conjecture for hyper-K"ahler manifolds

Insights into Voisin's conjecture on algebraic cycles

Analysis of birational invariants in hyper-K"ahler geometry

Abstract

This thesis is devoted to the study of algebraic cycles in projective hyper-K\"ahler manifolds and strict Calabi-Yau manifolds. It contributes to the understanding of Beauville's and Voisin's conjectures on the Chow rings of projective hyper-K\"ahler manifolds and strict Calabi-Yau manifolds. It also studies some birational invariants of projective hyper-K\"ahler manifolds.