We study deformations of invertible bimodules and the behavior of Picard groups under deformation quantization. While K0-groups are known to be stable under formal deformations of algebras, Picard groups may change drastically. We identify the semiclassical limit of bimodule deformations as contravariant connections and study the associated deformation quantization problem. Our main focus is on...

We classify all smooth projective horospherical varieties with Picard number 1. We prove that the automorphism group of any such variety X acts with at most two orbits and that this group still acts with only two orbits on X blown up at the closed orbit. We characterize all smooth projective two-orbits varieties with Picard number 1 that satisfy this latter property. Mathematics Subject Classif...

Snow melting bias in microwave mapping of Antarctic snow accumulation O. Magand, G. Picard, L. Brucker, M. Fily, and C. Genthon Laboratoire de Glaciologie et Géophysique de l’Environnement, CNRS, Université Joseph Fourier-Grenoble, 54 Rue Molière, BP 96, 38402 St Martin d’Hères Cedex, France Received: 13 February 2008 – Accepted: 4 March 2008 – Published: 24 April 2008 Correspondence to: G. Pic...

We compute all K3 surfaces with Picard rank 20 over Q. Our proof uses modularity, the Artin-Tate conjecture and class group theory. With different techniques, the result has been established by Elkies to show that Mordell-Weil rank 18 over Q is impossible for an elliptic K3 surface. We also apply our methods to general singular K3 surfaces, i.e. with geometric Picard rank 20, but not necessaril...

PARADIGM Akshay Mohan, Rosalind Picard The Media Laboratory, Massachusetts Institute of Technology 20 Ames Street, Cambridge MA 02139-4307 USA {amohan, picard}@media.mit.edu Abstract The paper describes Health0: an innovative healthcare and lifestyle management wearable system that aims to bring an individual focused approach to healthcare. A modular architecture is proposed that combines a Lin...

The Brauer group of a commutative ring is an important invariant of a commutative ring, a common journeyman to the group of units and the Picard group. Burnside rings of finite groups play an important rôle in representation theory, and their groups of units and Picard groups have been studied extensively. In this short note, we completely determine the Brauer groups of Burnside rings: they van...

A question arising out of the late 80’s about computation systems was could machines be intelligent without emotions ([Minsky 1988]). It seems that the machines of today are not only inhuman but also behave stupidly. Studies by psychologists have shown that humans who lack the emotional features usually used by many aspects of human reasoning do not behave intelligently [Damasio 1994]. This the...

Five dimensional supersymmetric gauge theory compactified on a circle defines an effective N = 2 supersymmetric theory for massless fields in four dimensions. Based on the relativistic Toda chain Hamiltonian proposed by Nekrasov, we derive the Picard-Fuchs equation on the moduli space of the Coulomb branch of SU(2) gauge theory. Our Picard-Fuchs equation agrees with those from other approaches;...

Fix a holomorphic line bundle ξ over a compact connected Riemann surface X of genus g, with g ≥ 2, and also fix an integer r such that degree(ξ) > r(2g−1). Let Mξ(r) denote the moduli space of stable vector bundles overX of rank r and determinant ξ. The Fourier–Mukai transform, with respect to a Poincaré line bundle on X × J(X), of any F ∈Mξ(r) is a stable vector bundle on J(X). This gives an e...

Why should a number theorist be interested in algebraic geometry? In this course we hope to demonstrate one very good reason, by showing essentially geometric reasons why certain Diophantine equations fail to have solutions. But we will begin by placing the study of Diophantine equations into the context of algebraic geometry, to see how techniques from many different realms of mathematics can ...