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

By Alexander Polishchuk

the purpose of this e-book is to give a contemporary remedy of the idea of theta features within the context of algebraic geometry. the newness of its procedure lies within the systematic use of the Fourier-Mukai rework. the writer begins through discussing the classical concept of theta features from the perspective of the illustration concept of the Heisenberg team (in which the standard Fourier rework performs the well known role). He then indicates that during the algebraic method of this conception, the Fourier–Mukai remodel can frequently be used to simplify the present proofs or to supply thoroughly new proofs of many vital theorems. Graduate scholars and researchers with robust curiosity in algebraic geometry will locate a lot of curiosity during this volume.

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