By Alexander Polishchuk

the purpose of this e-book is to offer a contemporary therapy of the speculation 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 by way of discussing the classical thought of theta features from the viewpoint of the illustration concept of the Heisenberg staff (in which the standard Fourier remodel performs the famous 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 robust curiosity in algebraic geometry will locate a lot of curiosity during this volume.

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