Grivaux, Julien  Variation of the holomorphic determinant bundle. (English) Zbl
Math. Res. Lett. 20, No. 6, ). Let f : X → Y be a proper holomorphic submersion between complex manifolds an

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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

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• Algebra
• Abstract algebra
• Geometry
• Algebraic geometry
• Vector bundles
• Algebraic varieties
• Projective geometry
• Bernhard Riemann
• Projective variety
• Kobayashi metric
• RiemannRoch theorem
• Canonical bundle

¨ HYPERKAHLER MANIFOLDS OLIVIER DEBARRE Abstract. The aim of these notes is to acquaint the reader with important objects in complex

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• Algebraic geometry
• Geometry
• Algebra
• Algebraic surfaces
• Birational geometry
• Algebraic curves
• Abelian varieties
• K3 surface
• Projective variety
• EnriquesKodaira classification
• Ample line bundle
• Enriques surface

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.

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• Algebra
• Abstract algebra
• Topology
• Vector bundles
• Algebraic geometry
• Complex manifolds
• Sheaf theory
• Algebraic topology
• Ample line bundle
• Holomorphic vector bundle
• Coherent sheaf
• Divisor

Grivaux, Julien Topological properties of Hilbert schemes of almost-complex fourfolds. I. (English) Zbl
Manuscr. Math. 136, No. 1-2, Given a smooth irreducible complex projective surface X,

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• Abstract algebra
• Algebra
• Mathematics
• Algebraic geometry
• Homological algebra
• Differential geometry
• Cohomology theories
• Projective variety
• Hilbert scheme
• Perverse sheaf
• Manifold
• tale cohomology

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

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• Geometry
• Algebraic geometry
• Abstract algebra
• Algebraic varieties
• Algebraic surfaces
• Hodge theory
• Fano variety
• Birational geometry
• Projective variety
• Hodge structure
• K3 surface
• Canonical bundle

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

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• Algebraic geometry
• Geometry
• Abstract algebra
• Birational geometry
• Algebraic varieties
• Vector bundles
• Divisor
• Projective variety
• Ample line bundle
• Algebraic surface
• Blowing up
• Exceptional divisor

Lipari School on Computational Complex and Social Systems: From swarm intelligence to digital democracy: new tools for a complex society JulyLipari Island, Italy SCHOOL SCHEDULE

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PERIODS OF ALGEBRAIC VARIETIES OLIVIER DEBARRE Abstract. The periods of a compact complex algebraic manifold X are the integrals of its holomorphic 1-forms over paths. These integrals are in general not well-defined, but

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• Geometry
• Abstract algebra
• Algebra
• Algebraic geometry
• Hodge theory
• Projective variety
• Hodge structure
• K3 surface
• Elliptic curve
• Algebraic variety
• Khler manifold
• Differential forms on a Riemann surface

CURVES OF LOW DEGREES IN FANO VARIETIES OLIVIER DEBARRE Abstract. We work over the complex numbers. Fano manifolds are smooth projective varieties whose canonical bundle is antiample. In dimensions at most 3, they are al

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• Abstract algebra
• Algebra
• Geometry
• Algebraic geometry
• Fano variety
• Birational geometry
• Divisor
• Projective variety
• Coherent sheaf
• Hodge structure
• Cohomology
• Ample line bundle