Work

Forms and complex manifolds

Year: 2025

Type: article

Abstract: We study the intersection form F_{X} on the second cohomology group H^{2}(X, \mathbb{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 \geq 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.

Source: EMS Surveys in Mathematical Sciences

DOI: 10.4171/emss/109

Authors: Cinzia Bisi, Paolo Cascini, Luca Tasin

Institutions: University of Ferrara, Imperial College London, University of Milan

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4417430374

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