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Olivier Debarre
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21	FAKE PROJECTIVE SPACES AND FAKE TORI OLIVIER DEBARRE Abstract. Hirzebruch and Kodaira proved in 1957 that when n is odd, any compact K¨ ahler manifold X which is homeomorphic to Pn is isomorphic to Pn . This holds for a Add to Reading List Source URL: www.math.ens.fr Language: English - Date: 2017-03-03 09:54:55 Algebra Abstract algebra Cohomology theories Algebraic geometry Homological algebra Birational geometry Algebraic surfaces Cohomology Projective variety Hodge theory tale cohomology Kodaira dimension
22	PERIODS AND MODULI OLIVIER DEBARRE Abstract. This text is an introduction, without proofs and by means of many examples, to some elementary aspects of the theory of period maps, period domains, and their relationship wit Add to Reading List Source URL: www.math.ens.fr Language: English - Date: 2012-09-23 09:53:30 Algebraic geometry Algebra Abstract algebra Algebraic curves Algebraic surfaces Moduli theory Hodge theory Projective variety Abelian variety Hodge structure Divisor Moduli space
23	¨ UNEXPECTED ISOMORPHISMS BETWEEN HYPERKAHLER FOURFOLDS OLIVIER DEBARRE Abstract. Using Verbitsky’s Torelli theorem, we show the existence of various isomorphisms between certain hyperk¨ Add to Reading List Source URL: www.math.ens.fr Language: English - Date: 2017-03-03 09:55:02 Topology Algebraic surfaces Geometry Algebraic geometry K3 surface Birational geometry Divisor Quartic surface Von Neumann algebra Hodge structure
24	HYPERBOLICITY Colloquium – University of Michigan March 9, 2004 Olivier Debarre There exist several notions of hyperbolicity for compact complex varieties and I will try to explain what they are and how they are relate Add to Reading List Source URL: www.math.ens.fr Language: English - Date: 2006-01-10 13:48:42 Algebra Abstract algebra Geometry Algebraic geometry Vector bundles Algebraic varieties Projective geometry Bernhard Riemann Projective variety Kobayashi metric RiemannRoch theorem Canonical bundle
25	¨ HYPERKAHLER MANIFOLDS OLIVIER DEBARRE Abstract. The aim of these notes is to acquaint the reader with important objects in complex Add to Reading List Source URL: www.math.ens.fr Language: English - Date: 2018-10-04 04:14:37 Algebraic geometry Geometry Algebra Algebraic surfaces Birational geometry Algebraic curves Abelian varieties K3 surface Projective variety EnriquesKodaira classification Ample line bundle Enriques surface
26	HYPERBOLICITY OF COMPLEX VARIETIES OLIVIER DEBARRE These are notes written for the 2004 session of the PRAGMATIC conference, held in Catania, Italy, from August 25 to September 14, 2004. Add to Reading List Source URL: www.math.ens.fr Language: English - Date: 2011-08-29 09:42:05 Algebra Abstract algebra Topology Vector bundles Algebraic geometry Complex manifolds Sheaf theory Algebraic topology Ample line bundle Holomorphic vector bundle Coherent sheaf Divisor
27	On the geometry of certain Fano threefolds Olivier DEBARRE Institut de Recherche Math´ ematique Avanc´ ee (IRMA) Add to Reading List Source URL: www.math.ens.fr Language: English - Date: 2007-05-07 12:44:04 Geometry Algebraic geometry Algebra Complex manifolds Riemannian geometry Fano variety Gino Fano Olivier Debarre Hermitian manifold Manifold Khler manifold
28	ON PRIME FANO VARIETIES OF DEGREE 10 AND COINDEX 3 OLIVIER DEBARRE Abstract. We discuss the period map of certain (complex) Fano varieties. The first part of this talk deals with cubic hypersurfaces. We recall their Hodg Add to Reading List Source URL: www.math.ens.fr Language: English - Date: 2012-09-27 08:07:55 Geometry Algebraic geometry Abstract algebra Algebraic varieties Algebraic surfaces Hodge theory Fano variety Birational geometry Projective variety Hodge structure K3 surface Canonical bundle
29	PERIODS OF CUBIC FOURFOLDS AND OF DEBARRE–VOISIN VARIETIES OLIVIER DEBARRE Abstract. Beauville and Donagi showed that the primitive Hodge structure of a smooth complex cubic hypersurface of dimension four is isomorphic Add to Reading List Source URL: www.math.ens.fr Language: English - Date: 2018-08-31 08:19:23 Algebraic geometry Geometry Abstract algebra Birational geometry Algebraic varieties Vector bundles Divisor Projective variety Ample line bundle Algebraic surface Blowing up Exceptional divisor
30	THE FANO THREEFOLD X10 OLIVIER DEBARRE This is joint work in progress with A. Iliev (Sofia) and L. Manivel (Grenoble). 1. Introduction Add to Reading List Source URL: www.math.ens.fr Language: English - Date: 2008-05-16 16:37:50 Algebraic geometry Abstract algebra Algebra Algebraic varieties Vector bundles Birational geometry Fano variety Divisor Cubic threefold Canonical bundle Sheaf Smooth scheme