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

By Alexander Polishchuk

the purpose of this booklet is to offer a latest therapy of the speculation of theta features within the context of algebraic geometry. the newness of its process lies within the systematic use of the Fourier-Mukai rework. the writer begins by means of discussing the classical concept of theta capabilities from the viewpoint of the illustration conception of the Heisenberg staff (in which the standard Fourier remodel performs the well-liked role). He then exhibits that during the algebraic method of this thought, the Fourier–Mukai remodel 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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