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MODSTABVAR SIGNED

Moduli spaces of stable varieties and applications

Total Cost €

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EC-Contrib. €

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Partnership

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 MODSTABVAR project word cloud

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

curvature    volume    bhatt    incarnation    classifies    metric    generalizations    macaulay    fundamental    base    possibly    compactification    guenancia    geometry    modern    projective    dimensions    philosophy    relative    grothendieck    latter    trace    right    vanishings    hler    hence    perfectoid       big    stable    itself    surprisingly    model    auml    smooth    shown    negative    torsion    equivalence    setting    provides    balanced    koll    classifying    moduli    canonically    statements    admitting    arithmetic    depending    algebras    algebro    minimal    lifting    theory    integers    positive    surfaces    showing    originally    perspectives    coarse    geometric    lack    primes    scholze    eacute    varieties    fixed    existence    algebraic    singular    odaka    einstein    berman    finitely    aacute    attain    conjectural    notion    dimensional    polarized    proved    cohomology    excluding    barron    cohen    shepherd    motivations    mixed    birational    space    alterations    curves    folds    torsor    construct    beginning    killing    sections    andr   

Project "MODSTABVAR" data sheet

The following table provides information about the project.

Coordinator
ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE 

Organization address
address: BATIMENT CE 3316 STATION 1
city: LAUSANNE
postcode: 1015
website: www.epfl.ch

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Switzerland [CH]
 Total cost 1˙201˙370 €
 EC max contribution 1˙201˙370 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2018-STG
 Funding Scheme ERC-STG
 Starting year 2020
 Duration (year-month-day) from 2020-03-01   to  2025-02-28

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE CH (LAUSANNE) coordinator 1˙201˙370.00

Map

 Project objective

Stable varieties, originally introduced by Kollár and Shepherd-Barron, are higher dimensional generalizations of the algebro-geometric notion of stable curves from many perspectives. Their partially conjectural moduli space classifies smooth projective varieties of general type up to birational equivalence, and it also provides a projective compactification for this classifying space. The latter is essential for applying algebraic geometry to the moduli space itself. Furthermore, over the complex numbers, stable varieties can be also defined surprisingly as the projective varieties admitting a negative curvature (singular) Kähler-Einstein metric by the work of Berman and Guenancia, or as the canonically polarized K-stable varieties by Odaka.

The fundamental objective of the project is to construct the coarse moduli space of stable surfaces with fixed volume over the integers (possibly excluding finitely many primes, not depending on the volume). In particular this involves showing the Minimal Model Program for 3-folds that are projective over a 1 dimensional mixed characteristic base. The main motivations are applications to the general algebraic geometry and arithmetic of higher dimensional varieties.

The above fundamental goal is also an incarnation of Grothendieck's philosophy that algebraic geometry statements should be proved in a relative setting. This was implemented right at the beginning for stable curves, but it has not been possible to attain for stable varieties of higher dimensions, due to the lack of technology. Hence, the project aims to establish new technology in mixed and positive characteristic geometry based on recent developments, such as modern Minimal Model Program, the vanishings given by balanced big Cohen-Macaulay algebras (the existence of which was shown by André using Scholze's perfectoid theory), trace method for lifting sections, p-torsion cohomology killing via alterations (by Bhatt), torsor method on singular varieties, etc.

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The information about "MODSTABVAR" are provided by the European Opendata Portal: CORDIS opendata.

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