Alexander Polishchuk's Abelian Varieties, Theta Functions and the Fourier Transform PDF

By Alexander Polishchuk

the purpose of this booklet is to offer a latest remedy of the idea of theta capabilities within the context of algebraic geometry. the newness of its technique lies within the systematic use of the Fourier-Mukai remodel. the writer starts off via discussing the classical idea of theta services from the perspective of the illustration concept of the Heisenberg staff (in which the standard Fourier rework performs the well-liked role). He then exhibits that during the algebraic method of this thought, the Fourier–Mukai rework can frequently be used to simplify the present proofs or to supply thoroughly new proofs of many vital theorems. Graduate scholars and researchers with powerful curiosity in algebraic geometry will locate a lot of curiosity during this volume.

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Abelian Varieties, Theta Functions and the Fourier Transform (Cambridge Tracts in Mathematics) by Alexander Polishchuk

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