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Download Abelian Varieties, Theta Functions and the Fourier Transform by Alexander Polishchuk PDF

By Alexander Polishchuk

the purpose of this publication is to provide a latest remedy of the speculation of theta services within the context of algebraic geometry. the newness of its process lies within the systematic use of the Fourier-Mukai rework. the writer starts off via discussing the classical concept of theta features from the viewpoint of the illustration concept of the Heisenberg workforce (in which the standard Fourier remodel performs the renowned role). He then indicates that during the algebraic method of this idea, the Fourier–Mukai rework can frequently be used to simplify the present proofs or to supply thoroughly new proofs of many very important theorems. Graduate scholars and researchers with robust curiosity in algebraic geometry will locate a lot of curiosity during this volume.

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