We study the intersection form $F_X$ on the second cohomology group $H^2(X,Z)$ of a compact Kähler manifold X of dimension n. Although the structure of $F_X$ is relatively well understood in dimensions two and three, much less is known for $n≥4$. We investigate the fundamental properties of $F_X$ in higher dimensions and discuss several applications to birational geometry. Finally, we present a number of open problems concerning the relationship between birational invariants and topological invariants of Kähler manifolds.
Forms and Complex Manifolds
Cinzia Bisi;
2025
Abstract
We study the intersection form $F_X$ on the second cohomology group $H^2(X,Z)$ of a compact Kähler manifold X of dimension n. Although the structure of $F_X$ is relatively well understood in dimensions two and three, much less is known for $n≥4$. We investigate the fundamental properties of $F_X$ in higher dimensions and discuss several applications to birational geometry. Finally, we present a number of open problems concerning the relationship between birational invariants and topological invariants of Kähler manifolds.File in questo prodotto:
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