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Moduli spaces of stable varieties and applications

Project description

Constructing moduli spaces of high dimensional algebraic varieties

Introduced by Kollár and Shepherd-Barron, stable varieties are higher-dimensional generalisations of stable curves in algebraic geometry. Their conjectural moduli space classifies smooth projective varieties up to birational equivalence, while also providing a projective compactification. The latter is essential for applying algebraic geometry to the moduli space itself. The EU-funded MODSTABVAR project will construct the coarse moduli space of stable surfaces with fixed volume over the integers. This involves showing the minimal model program for three-dimensional algebraic variety that is projective over a one-dimensional mixed characteristic base. Project results will be very important to the fields of algebraic geometry and the arithmetic of higher-dimensional varieties.

Field of science

  • /natural sciences/mathematics/pure mathematics/algebra
  • /natural sciences/mathematics/pure mathematics/arithmetic
  • /natural sciences/mathematics/pure mathematics/geometry
  • /humanities/philosophy, ethics and religion/philosophy
  • /natural sciences/mathematics/pure mathematics/algebra/algebraic geometry

Call for proposal

ERC-2018-STG
See other projects for this call

Funding Scheme

ERC-STG - Starting Grant

Host institution

ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE
Address
Batiment Ce 3316 Station 1
1015 Lausanne
Switzerland
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 1 201 370

Beneficiaries (1)

ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE
Switzerland
EU contribution
€ 1 201 370
Address
Batiment Ce 3316 Station 1
1015 Lausanne
Activity type
Higher or Secondary Education Establishments