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Algebraic and Kähler geometry

The purpose of this project is to study basic questions in algebraic and Kähler geometry. It is well known that the structure of projective or Kähler manifolds is governed by positivity or negativity properties of the curvature te... ver más

31/08/2021

UGA

2M€

Presupuesto del proyecto: 2M€

Líder del proyecto

UNIVERSITE GRENOBLE ALPES No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Fecha límite participación Sin fecha límite de participación.

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Financiación concedida El organismo H2020 notifico la concesión del proyecto el día 2021-08-31

ERC-ADG-2014: ERC Advanced Grant

I+D

Cerrada hace 10 años

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2 Participantes

UGA

1.81M€ | Lider

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Duración del proyecto: 73 meses Fecha Inicio: 2015-07-02
Fecha Fin: 2021-08-31

Líder del proyecto

UNIVERSITE GRENOBLE ALPES No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Presupuesto del proyecto 2M€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto The purpose of this project is to study basic questions in algebraic and Kähler geometry. It is well known that the structure of projective or Kähler manifolds is governed by positivity or negativity properties of the curvature tensor. However, many fundamental problems are still wide open. Since the mid 1980's, I have developed a large number of key concepts and results that have led to important progress in transcendental algebraic geometry. Let me mention the discovery of holomorphic Morse inequalities, systematic applications of L² estimates with singular hermitian metrics, and a much improved understanding of Monge-Ampère equations and of singularities of plurisuharmonic functions. My first goal will be to investigate the Green-Griffiths-Lang conjecture asserting that an entire curve drawn in a variety of general type is algebraically degenerate. The subject is intimately related to important questions concerning Diophantine equations, especially higher dimensional generalizations of Faltings' theorem - the so-called Vojta program. One can rely here on a breakthrough I made in 2010, showing that all such entire curves must satisfy algebraic differential equations. A second closely related area of research of this project is the analysis of the structure of projective or compact Kähler manifolds. It can be seen as a generalization of the classification theory of surfaces by Kodaira, and of the more recent results for dimension 3 (Kawamata, Kollár, Mori, Shokurov, ...) to other dimensions. My plan is to combine powerful recent results obtained on the duality of positive cohomology cones with an analysis of the instability of the tangent bundle, i.e. of the Harder-Narasimhan filtration. On these ground-breaking questions, I intend to go much further and to enhance my national and international collaborations. These subjects already attract many young researchers and postdocs throughout the world, and the grant could be used to create even stronger interactions.

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