By Alexander Polishchuk

The purpose of this publication is to give a latest therapy of the speculation of theta services within the context of algebraic geometry. the newness of its process lies within the systematic use of the Fourier-Mukai remodel. the writer starts off through discussing the classical thought of theta capabilities from the viewpoint of the illustration thought of the Heisenberg staff (in which the standard Fourier remodel performs the in demand role). He then indicates that during the algebraic method of this thought, the Fourierâ€“Mukai rework can usually be used to simplify the prevailing 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 quantity.

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