"Topological, Algebraic, Differential Methods in Classification and Moduli Theory"

Cel

"Moduli of curves with symmetries:determine the stable irreducible components of the moduli space of curves of genus g with an action of a finite group G, using a new homological invariant. Stable means: for g sufficiently large, or for sufficiently large numerical branching function. Higher homological stabilization for these moduli spaces. Faithful actions of the absolute Galois group on moduli spaces of marked varieties, triangle curves, varieties isogenous to a product, Beauville surfaces. Change of fundamental group. Fields of definitions of triangle curves and the scheme representing triangle curves.
Uniformization: characterization of proj. var. whose universal cover is a given bounded symmetric domain (Catanese-Di Scala did the case of tube domains). Orbifold Uniformization: where we have a quotient of a non free action, or a noncompact such quotient. Classification of surfaces with genus 0 having the bidisk as universal cover. Symmetric differentials and fundamental groups of some ball quotients.
Topological methods in Moduli Theory: strong, weak and pseudo rigidity for the Inoue type varieties of Bauer and Catanese (free quotients of ample divisors on projective varieties which are K(\pi, 1)). With Lonne and Wajnryb, using methods by Auroux and Katzarkov: study canonical symplectic structures and deformation types of some simply connected algebraic surfaces, determining braid group factorizations associated to subcanonical projections. More general bicoloured braid factorizations associated to general projections. Teichmueller space of certain algebraic surfaces.
Classification and Moduli of surfaces with low invariants. Surfaces of geometric genus 0: new construction techniques, structure of fundamental groups, moduli spaces, existence questions for surfaces with certain invariants, for homotopy quadrics, structure of fake quadrics."

System finansowania

ERC-AG - ERC Advanced Grant

Instytucja przyjmująca

UNIVERSITAT BAYREUTH

Wkład UE

€ 1 725 420,00

Adres

UNIVERSITATSSTRASSE 30
95447 Bayreuth
Niemcy

Region

Bayern Oberfranken Bayreuth, Kreisfreie Stadt

Rodzaj działalności

Higher or Secondary Education Establishments

Kontakt administracyjny

Marcus Urban

Kierownik naukowy

Fabrizio Catanese (Prof.)

Linki

Kontakt z organizacją Strona internetowa

Koszt całkowity

Brak danych

Beneficjenci (1)