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# Documents  Catanese, Fabrizio | enregistrements trouvés : 4

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## Symplectic 4-manifolds and algebraic surfaces :lectures given at the C.I.M.E. summer school held in Cetraro#Sept. 2-10 Auroux, Denis ; Catanese, Fabrizio ; Manetti, Marco ; Seidel, Paul | Springer 2008

Congrès

- 341 p.
ISBN 978-3-540-78278-0

Lecture notes in mathematics , 1938

Localisation : Collection 1er étage

géométrie algébrique # surface algébrique # géométrie symplectique # déformation # surface de Reimann # théorie de Teichmüller # groupe de Braid # groupe de Artin

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## New trends in algebraic geometry :Euroconference on algebraic geometry#July Catanese, Fabrizio ; Hulek, Klaus ; Peters, Chris ; Reid, Miles | Cambridge University Press 1999

Congrès

- 484 p.
ISBN 978-0-521-64659-8

London mathematical society lecture note series , 0264

Localisation : Collection 1er étage

approche Lagrangienne # classification des surfaces # groupe de Crémone # géométrie algébrique # géométrie de la physique # géométrie symplectique # schéma de G-Hilbert # structure de Hodge # surface algébrique # symétrie du miroir # transformation d'espèces # transformée de Fourier-Mukai # treillis

14-06

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## Arithmetic geometry :I.N.D.A.M. symposium on... took place in the "Palazzone" of the Scuola Normale at Arezzo#Oct. 16-21 Catanese, Fabrizio | Cambridge University Press 1997

Congrès

ISBN 978-0-521-59133-1

Symposia mathematica , 0037

Localisation : Collection 1er étage

caractère de Hecke # construction de courbe # corps fini # corps quadratique # courbe # déterminant de cohomologie # géométrie algébrique # géométrie de l'arithmétique # géométrie différentielle algébrique # géométrie diophantienne # théorie des nombres # topologie étale

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## New examples of rigid varieties and criteria for fibred surfaces to be $K(\pi,1)$-spaces Catanese, Fabrizio | CIRM H

Multi angle

Research talks;Algebraic and Complex Geometry

Given an algebraic variety defined by a set of equations, an upper bound for its dimension at one point is given by the dimension of the Zariski tangent space. The infinitesimal deformations of a variety $X$ play a somehow similar role, they yield the Zariski tangent space at the local moduli space, when this exists, hence one gets an efficient way to estimate the dimension of a moduli space.
It may happen that this moduli space consists of a point, or even a reduced point if there are no infinitesimal deformations. In this case one says that $X$ is rigid, respectively inifinitesimally rigid.
A basic example is projective space, which is the only example in dimension 1. In the case of surfaces, infinitesimally rigid surfaces are either the Del Pezzo surfaces of degree $\ge$ 5, or are some minimal surfaces of general type.
As of now, the known surfaces of the second type are all projective classifying spaces (their universal cover is contractible), and have universal cover which is either the ball or the bidisk (these are the noncompact duals of $P^2$ and $P^1 \times P^1$ ), or are the examples of Mostow and Siu, or the Kodaira fibrations of Catanese-Rollenske.
Motivated by recent examples constructed with Dettweiller of interesting VHS over curves, which we shall call BCD surfaces, together with ingrid Bauer, we showed the rigidity of a class of surfaces which includes the Hirzebruch-Kummer coverings of the plane branched over a complete quadrangle.
I shall also explain some results concerning fibred surfaces, e.g. a criterion for being a $K(\pi,1)$-space; I will finish mentioning other examples and several interesting open questions.
Given an algebraic variety defined by a set of equations, an upper bound for its dimension at one point is given by the dimension of the Zariski tangent space. The infinitesimal deformations of a variety $X$ play a somehow similar role, they yield the Zariski tangent space at the local moduli space, when this exists, hence one gets an efficient way to estimate the dimension of a moduli space.
It may happen that this moduli space consists of a ...

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