منابع مشابه
Generalized Unitaries and the Picard Group
After discussing some basic facts about generalized module maps, we use the representation theory of the algebra Ba(E) of adjointable operators on a Hilbert B–module E to show that the quotient of the group of generalized unitaries on E and its normal subgroup of unitaries on E is a subgroup of the group of automorphisms of the range ideal BE of E in B. We determine the kernel of the canonical ...
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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 ...
متن کاملThe Picard Group of a Loop Space
The loop space LP1 of the Riemann sphere consisting of all C k or Sobolev W k,p maps S → P1 is an infinite dimensional complex manifold. We compute the Picard group Pic(LP1) of holomorphic line bundles on LP1 as an infinite dimensional complex Lie group with Lie algebra the Dolbeault group H(LP1). The group of Möbius transformations G and its loop group LG act on LP1. We prove that an element o...
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We explicitly compute the elliptic points and isotropy groups for the action of the Picard modular group over the Gaussian integers on 2-dimensional complex hyperbolic space.
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We test the methods for computing the Picard group of a K3 surface in a situation of high rank. The examples chosen are resolutions of quartics in P having 14 singularities of type A1. Our computations show that the method of R. van Luijk works well when sufficiently large primes are used.
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ژورنال
عنوان ژورنال: Proceedings of the Indian Academy of Sciences - Section A
سال: 2006
ISSN: 0370-0089
DOI: 10.1007/bf02829701