Download e-book for kindle: Compact Riemann Surfaces by R. Narasimhan

By R. Narasimhan

ISBN-10: 3034886179

ISBN-13: 9783034886178

ISBN-10: 3764327421

ISBN-13: 9783764327422

Those notes shape the contents of a Nachdiplomvorlesung given on the Forschungs institut fur Mathematik of the Eidgenossische Technische Hochschule, Zurich from November, 1984 to February, 1985. Prof. ok. Chandrasekharan and Prof. Jurgen Moser have inspired me to put in writing them up for inclusion within the sequence, released by way of Birkhiiuser, of notes of those classes on the ETH. Dr. Albert Stadler produced exact notes of the 1st a part of this path, and extremely intelligible class-room notes of the remaining. with no this paintings of Dr. Stadler, those notes do not have been written. whereas i've got replaced a few issues (such because the facts of the Serre duality theorem, right here performed totally within the spirit of Serre's unique paper), the current notes keep on with Dr. Stadler's particularly heavily. My unique objective in giving the path used to be twofold. i needed to offer the elemental theorems in regards to the Jacobian from Riemann's personal perspective. Given the Riemann-Roch theorem, if Riemann's equipment are expressed in sleek language, they fluctuate little or no (if in any respect) from the paintings of recent authors.

Show description

Read Online or Download Compact Riemann Surfaces PDF

Similar calculus books

Download e-book for kindle: Student's Guide to Basic Multivariable Calculus by Karen Pao, Frederick Soon

Designed as a better half to easy Multivariable Calculus via Marsden, Tromba, and Weinstein. This booklet parallels the textbook and reinforces the suggestions brought there with routines, examine tricks, and quizzes. specific suggestions to difficulties and ridicule examinations also are integrated.

Takasi Senba's Applied Analysis: Mathematical Methods in Natural Science PDF

Senba (Miyazaki U. ) and Suzuki (Osaka U. ) offer an creation to utilized arithmetic in quite a few disciplines. issues contain geometric gadgets, reminiscent of easy notions of vector research, curvature and extremals; calculus of version together with isoperimetric inequality, the direct and oblique tools, and numerical schemes; endless dimensional research, together with Hilbert house, Fourier sequence, eigenvalue difficulties, and distributions; random movement of debris, together with the method of diffusion, the kinetic version, and semiconductor gadget equations; linear and non-linear PDE theories; and the approach of chemotaxis.

Download e-book for kindle: Differential and Integral Calculus [Vol 1] by Richard Courant

This set good points: Foundations of Differential Geometry, quantity 1 by way of Shoshichi Kobayashi and Katsumi Nomizu (978-0-471-15733-5) Foundations of Differential Geometry, quantity 2 through Shoshichi Kobayashi and Katsumi Nomizu (978-0-471-15732-8) Differential and fundamental Calculus, quantity 1 by means of Richard Courant (978-0-471-60842-4) Differential and vital Calculus, quantity 2 by way of Richard Courant (978-0-471-60840-0) Linear Operators, half 1: basic concept through Neilson Dunford and Jacob T.

Download e-book for iPad: Asymptotic Approximation of Integrals by R. Wong

Asymptotic tools are often utilized in many branches of either natural and utilized arithmetic, and this vintage textual content is still the main updated publication facing one very important element of this quarter, specifically, asymptotic approximations of integrals. during this ebook, all effects are proved conscientiously, and plenty of of the approximation formulation are observed by means of blunders bounds.

Additional info for Compact Riemann Surfaces

Example text

2, these sections cannot have common zeros. (s;g} : ... : Note. If L is a holomorphic line bundle on X and HO(X, L) f. pL: X --+ JlDN (N = dimHO(X,L) -1) on all of X. If So, ... ,SN is a basis as above and A = {x E X I S j (x) = Vj }, the map is defined as above on X - A. p L I U - {a} is the point in JlDN with homogeneous coordinates (10 : ... : fN) where fo, .. ·, fN are holomorphic functions on U and are not outside a. We can write fj = Zk gj where k = minj ord a (1j). p L on U is then given by the point in JlDN with homogeneous coordinates (go: ...

Then h 0 sex) = (x,f(x)), x E U, where f is an n-tuple of meromorphic functions on U. There is an integer k such that f = zk g, where g is an n-tuple of functions holomorphic near a, and g(a) "I- o. We set k = orda(s). One checks easily that this is independent of the local coordinate and of the local trivialisation. e. the divisor L f-+ ord a (s), orda(s)a , aEX is called the divisor of s and denoted by (s) or dives). e. vector bundle of rank 1), and we turn now to this construction. Let X be a Riemann surface and D a divisor on X; let D = LPEX npP (where np = D(P) E Z and the sum is locally finite).

If a E X, and i is such that a E Ui , set resa(w) = resa(wi) [this is independent of i because Wi - Wj is holomorphic on Ui n Uj]. Ui = [}Oi = dO i represents the cohomology class D({Wij}) in A~~(X) under the Dolbeault isomorphism. We have Lemma. Jx D ({Wij}) = 27ri LaEX resa(w) . Proof. Let (3 = Wi - 0i on Ui ; (3 is a Coo form on X - {al,"" an}, where S = {al,"" aT} is the set of poles of w (S n Ui = set of poles of Wi). Since dWi = 0 on Ui - S, we have cp = D({Wij}) = -d(3 on X - S. e = 1, ...

Download PDF sample

Compact Riemann Surfaces by R. Narasimhan


by Anthony
4.4

Rated 4.65 of 5 – based on 24 votes