| Riemann Surfaces and Generalized Theta Functions Softcover Repri Edition Contributor(s): Gunning, Robert C. (Author) |
|
 |
ISBN: 3642663842 ISBN-13: 9783642663840 Publisher: Springer OUR PRICE: $52.24 Product Type: Paperback - Other Formats Published: December 2011 |
| Additional Information |
| BISAC Categories: - Mathematics | Transformations - Mathematics | Mathematical Analysis |
| Dewey: 515.73 |
| Series: Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 2. Folge |
| Physical Information: 0.39" H x 6.69" W x 9.61" (0.67 lbs) 168 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |