Download E-books Abelian Varieties, Theta Functions and the Fourier Transform (Cambridge Tracts in Mathematics) PDF

By Alexander Polishchuk

This ebook is a contemporary remedy of the speculation of theta features within the context of algebraic geometry. the newness of its process lies within the systematic use of the Fourier-Mukai rework. Alexander Polishchuk starts off through discussing the classical conception of theta services from the point of view of the illustration idea of the Heisenberg workforce (in which the standard Fourier remodel performs the favourite role). He then exhibits that during the algebraic method of this conception (originally as a result of Mumford) the Fourier-Mukai rework can usually be used to simplify the present proofs or to supply thoroughly new proofs of many vital theorems. This incisive quantity is for graduate scholars and researchers with powerful curiosity in algebraic geometry.

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