By Alexander Polishchuk
The purpose of this booklet is to give a latest 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 via discussing the classical idea of theta services from the viewpoint of the illustration conception of the Heisenberg team (in which the standard Fourier rework performs the famous role). He then exhibits that during the algebraic method of this idea, the Fourier–Mukai remodel 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 robust curiosity in algebraic geometry will locate a lot of curiosity during this quantity.
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