By Alexander Polishchuk

the purpose of this publication is to give a contemporary remedy of the speculation of theta capabilities 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 thought of theta services from the viewpoint of the illustration idea of the Heisenberg team (in which the standard Fourier rework performs the in demand role). He then exhibits that during the algebraic method of this conception, the Fourier–Mukai rework can usually be used to simplify the present proofs or to supply thoroughly new proofs of many very important theorems. Graduate scholars and researchers with powerful curiosity in algebraic geometry will locate a lot of curiosity during this volume.

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