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By Alexander Polishchuk

the purpose of this booklet is to give a contemporary remedy of the speculation of theta services within the context of algebraic geometry. the newness of its strategy lies within the systematic use of the Fourier-Mukai remodel. the writer begins by means of discussing the classical concept of theta capabilities from the perspective of the illustration thought of the Heisenberg crew (in which the standard Fourier remodel performs the favourite role). He then exhibits that during the algebraic method of this idea, the Fourier–Mukai rework can usually 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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