The investigation of the relationships between compact Riemann surfaces (al- gebraic curves) and their associated complex tori (Jacobi varieties) has long been basic to the study both of Riemann surfaces and of complex tori. A Riemann surface is naturally imbedded as an analytic submanifold in its associated torus; and various spaces of linear equivalence elasses of divisors on the surface (or equivalently spaces of analytic equivalence elasses of complex line bundies over the surface), elassified according to the ...
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The investigation of the relationships between compact Riemann surfaces (al- gebraic curves) and their associated complex tori (Jacobi varieties) has long been basic to the study both of Riemann surfaces and of complex tori. A Riemann surface is naturally imbedded as an analytic submanifold in its associated torus; and various spaces of linear equivalence elasses of divisors on the surface (or equivalently spaces of analytic equivalence elasses of complex line bundies over the surface), elassified according to the dimensions of the associated linear series (or the dimensions of the spaces of analytic cross-sections), are naturally realized as analytic subvarieties of the associated torus. One of the most fruitful of the elassical approaches to this investigation has been by way of theta functions. The space of linear equivalence elasses of positive divisors of order g -1 on a compact connected Riemann surface M of genus g is realized by an irreducible (g -1)-dimensional analytic subvariety, an irreducible hypersurface, of the associated g-dimensional complex torus J(M); this hyper- 1 surface W- r;;;, J(M) is the image of the natural mapping Mg- -+J(M), and is g 1 1 birationally equivalent to the (g -1)-fold symmetric product Mg- jSg-l of the Riemann surface M.
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Add this copy of Ergebnisse Der Mathematik Und Ihrer Grenzgebiete: to cart. $31.79, good condition, Sold by Anybook rated 4.0 out of 5 stars, ships from Lincoln, UNITED KINGDOM, published 1976 by Springer-Verlag.
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Volume 91. This is an ex-library book and may have the usual library/used-book markings inside. This book has hardback covers. In good all round condition. No dust jacket. Please note the Image in this listing is a stock photo and may not match the covers of the actual item, 500grams, ISBN: 3540077448.
Add this copy of Riemann Surfaces and Generalized Theta Functions to cart. $60.65, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2011 by Springer.
Add this copy of Riemann Surfaces and Generalized Theta Functions to cart. $87.09, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 2011 by Springer.
