We prove that the adelic Picard group of holomorphic line bundles is isomorphic to the rationals and prove the Birkhoff-Grothendieck splitting theorem for holomorphic bundles of higher rank over P. The paper on the subject appears in arXiv: arXiv:2001 . Mat. Constructions and Obstructions in Birational Geometry La mathématicienne Claire Voisin, entre formes et équations Advances in geometric analysis. Our method is based on the following result which allows to give in section 1 a Our approach to stable birational types relies on the Grothendieck ring of vari-eties, the Larsen-Lunts Theorem [LL03] and the specialization map [NS17, KT17]. College de France Research Area Algebraic geometry Visit Tuesday, May 9, 2017 to Thursday, May 11, 2017 Location MS 6627 Website Kähler geometry is a natural extension of complex projective geometry where the tools of Hodge theory are still available and allow to study the link between topology and complex geometry. This includes techniques for compu-ting the re ned Euler characteristic of a smooth projective variety, and re ned The part of the text which most concerns you is on pages 832-38, 1108-10, 1170-73. The class of the affine line is a zero divisor in the Grothendieck ring ... Olivier Debarre, Lawrence Ein, Robert Lazarsfeld and Claire Voisin Abstract We study the cones of pseudoe ective and nef cycles of higher codimension on the self product of an elliptic curve with complex multiplication, and on the product of a very . Derived categories and Chow groups of hyperkaehler and Calabi-Yau ... Claire Voisin (Centre de math´ematiques Laurent Schwartz, CNRS UMR 7640, École Polytechnique, Palaiseau, France) . We also propose a substantial number of open problems for further investigation. Leila Schneps (Author of Math on Trial) - Goodreads AMS :: Journal of Algebraic Geometry Politec. Feb 5, 1986. If X is a smooth variety over the complex numbers, you can use the topological Euler characteristic of the support X ( C) of the scheme. this last fact, by the Hodge-Grothendieck conjecture and the Bloch conjecture. Born on March 4, 1962 at Saint-Leu-la-Forêt, near Paris, Claire Voisin joined the science division of the École normale supérieure de Sèvres in 1981. Weakstabilityconditions In this section, we review the notion of a weak stability condition on the derived category of coherent sheaves on a smooth threefold. Abstract: We use specialization for the Grothendieck ring of varieties to show that smooth Fano hypersurfaces of large degree are not in general stably birational to each other.