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Algebraic and Kähler geometry

Total Cost €


EC-Contrib. €






 ALKAGE project word cloud

Explore the words cloud of the ALKAGE project. It provides you a very rough idea of what is the project "ALKAGE" about.

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Project "ALKAGE" data sheet

The following table provides information about the project.


There are not information about this coordinator. Please contact Fabio for more information, thanks.

 Coordinator Country France [FR]
 Project website
 Total cost 1˙809˙345 €
 EC max contribution 1˙809˙345 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2014-ADG
 Funding Scheme ERC-ADG
 Starting year 2015
 Duration (year-month-day) from 2015-09-01   to  2020-08-31


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    UNIVERSITE GRENOBLE ALPES FR (GRENOBLE) coordinator 1˙809˙345.00


 Project objective

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.


year authors and title journal last update
List of publications.
2017 Hervé Gaussier, Xianghong Gong
Smooth equivalence of deformations of domains in complex euclidean spaces
published pages: , ISSN: , DOI:
arXiv preprint 2020-04-09
2017 Philipp Naumann
An approach to Griffiths conjecture
published pages: , ISSN: , DOI:
arXiv preprint 2020-04-09
2017 Junyan Cao; Jean-Pierre Demailly; Shin-ichi Matsumura
A general extension theorem for cohomology classes on non reduced analytic spaces: dedicated to the memory of Professor Qikeng Lu
published pages: , ISSN: 1674-7283, DOI: 10.1007/s11425-017-9066-0
Science China Mathematics periodical, volume 60 2020-04-09
2017 Long Li
Regularization of plurisubharmonic functions with a net of good points
published pages: , ISSN: , DOI:
arXiv preprint 2020-04-09
2017 Long Li
Strict convexity of the Mabuchi functional for energy minimizers
published pages: , ISSN: , DOI:
arXiv preprint 2020-04-09
2017 Hai Lin, Tao Zheng
Higher dimensional generalizations of twistor spaces
published pages: 492-505, ISSN: 0393-0440, DOI: 10.1016/j.geomphys.2016.12.018
Journal of Geometry and Physics 114 2020-04-09
2017 Filippo Bracci, Hervé Gaussier
A proof of the Muir–Suffridge conjecture for convex maps of the unit ball in $${mathbb {C}}^n$$ C n
published pages: , ISSN: 0025-5831, DOI: 10.1007/s00208-017-1581-8
Mathematische Annalen 2020-04-09
2017 Young-Jun Choi
Positivity of direct images of fiberwise Ricci-flat metrics on Calabi-Yau fibrations
published pages: , ISSN: , DOI:
arXiv preprint 2020-04-09
2017 Deng, Ya
Applications of the Ohsawa-Takegoshi Extension Theorem to Direct Image Problems
published pages: , ISSN: , DOI:
2017 2 2020-04-09
2017 Deng, Ya
On the Diverio-Trapani Conjecture
published pages: , ISSN: , DOI:
2017 1 2020-04-09
2017 Druel Stéphane
Some remarks on regular foliations with numerically trivial canonical class
published pages: 1-20, ISSN: 2491-6765, DOI:
EPIGA 1, article Nr 4 2020-04-09
2017 Druel, Stéphane, Araujo, Carolina
Characterization of generic projective space bundles and algebraicity of foliations
published pages: 13 pages, ISSN: , DOI:
arXiv preprint November 2017 2020-04-09
2018 Demailly, Jean-Pierre
Recent results on the Kobayashi and Green-Griffiths-Lang conjectures
published pages: , ISSN: , DOI: 1 2020-04-09
2018 Tao Zheng
An Almost Complex Chern–Ricci Flow
published pages: 2129-2165, ISSN: 1050-6926, DOI: 10.1007/s12220-017-9898-9
The Journal of Geometric Analysis 28/3 2020-04-09
2018 Jean-Pierre Demailly, Mohammad Reza Rahmati
Morse cohomology estimates for jet differential operators
published pages: , ISSN: 1972-6724, DOI: 10.1007/s40574-018-0172-2
Bollettino dell\'Unione Matematica Italiana 2020-04-09
2018 Beffara, Vincent; Gayet, Damien
Percolation without FKG
published pages: , ISSN: , DOI:
IF_PREPUB. 2018 3 2020-04-09

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