Posted in Algebraic Geometry

Get Lectures on moduli of curves PDF

By D. Gieseker

ISBN-10: 0387119531

ISBN-13: 9780387119533

ISBN-10: 3540119531

ISBN-13: 9783540119531

Those notes are in response to a few lectures given at TIFR in the course of January and February 1980. the thing of the lectures was once to build a projectire moduli house for good curves of genus g >= 2 utilizing Mumford's geometric' invariant thought.

Show description

Read Online or Download Lectures on moduli of curves PDF

Best algebraic geometry books

Masaki Kashiwara, Pierre Schapira's Sheaves on manifolds PDF

From the reports: This ebook is dedicated to the learn of sheaves by way of microlocal equipment. .(it) may possibly function a reference resource in addition to a textbook in this new topic. Houzel's historic evaluation of the advance of sheaf thought will determine vital landmarks for college kids and should be a excitement to learn for experts.

Haruzo Hida's Geometric Modular Forms and Elliptic Curves PDF

This booklet presents a accomplished account of the speculation of moduli areas of elliptic curves (over integer earrings) and its software to modular varieties. the development of Galois representations, which play a basic position in Wiles' evidence of the Shimura-Taniyama conjecture, is given. furthermore, the booklet provides an overview of the facts of numerous modularity result of two-dimensional Galois representations (including that of Wiles), in addition to the various author's new leads to that course.

David Mumford, M. Nori, P. Norman's Tata Lectures on Theta III PDF

The second one in a chain of 3 volumes surveying the idea of theta capabilities, this quantity offers emphasis to the distinct homes of the theta capabilities linked to compact Riemann surfaces and the way they result in strategies of the Korteweg-de-Vries equations in addition to different non-linear differential equations of mathematical physics.

K. A. Ribet's Current Trends in Arithmetical Algebraic Geometry PDF

Mark Sepanski's Algebra is a readable creation to the pleasant global of contemporary algebra. starting with concrete examples from the learn of integers and modular mathematics, the textual content gradually familiarizes the reader with larger degrees of abstraction because it strikes in the course of the research of teams, jewelry, and fields.

Additional info for Lectures on moduli of curves

Sample text

Let RI be an unbounded simply connected open region in the complex plane which does not contain the roots e l , e z , e 3 of the cubic 4x 3 - g2 X - g3' 28 I. 11 For uER 1, defme a function z = g(u) by where a fixed branch of the square root is chosen as t varies in R 1 • Note that the integral converges and is independent of the path in Rl from u to 00, since Rl is simply connected. The function z = g(u) can be analytically continued by letting R z be a simply connected region in IC - {e 1 , ez , e 3 } which overlaps with R 1 • If uER z , then choose uIERlnRz, and set z=g(u)=g(ul)+S~'(4t3_gzt­ g3)-I/zdt.

If yZ = x 3 - 112 x gives an elliptic curve over IFp. More generally, if yZ = f(x) is an elliptic curve E defined over an algebraic number field, and if p is a prime ideal of the number field which does not divide the denominators of the coefficients of f(x) or the discriminant of f(x) , then by reduction modulo p we obtain an elliptic curve defined over the (finite) residue field of p. At first glance, it may seem that the elliptic curves over finite fieldswhich lead only to finite abelian groups-are not a serious business, and that reduction modulo p is a frivolous game that will not help us in our original objective of studying i1J-points on yZ = x 3 - I1zX.

Y2' j\Z2) = (0, )li5'2' )l2 Zl) = (0,)11' Zl) = PI (where we have used the fact that p divides Y l Z2 - Y2Zl)' (ii)p does not divide Xl' Then P2 = (XlX2,Xl)l2,XlZ2) = (X l X2,X2)1l' X2Z1) = (Xl' )11' Zl) = Pl' Conversely, suppose that PI = P2 . , if p divides X 1Y2 - X2Yl and X1Z2 - X2Z1. Finally, we must show thatp divides Yl Z2 - Y2 Zl' If both Yl and Z1 are divisible by p, then this is trivial. Otherwise, the conclusion will follow by repeating the above argument with Xl' x 2 replaced by Yl' Y2 or by Zl' Z2' This concludes the proof of the lemma.

Download PDF sample

Lectures on moduli of curves by D. Gieseker


by Thomas
4.5

Rated 4.14 of 5 – based on 45 votes