Algebraic Geometry

Download E-books Moduli of Curves (Graduate Texts in Mathematics) PDF

By Joe Harris

A advisor to a wealthy and engaging topic: algebraic curves and the way they range in households. supplying a wide yet compact review of the sphere, this e-book is on the market to readers with a modest historical past in algebraic geometry. It develops many suggestions, together with Hilbert schemes, deformation thought, solid aid, intersection conception, and geometric invariant conception, with the point of interest on examples and functions bobbing up within the examine of moduli of curves. From such foundations, the e-book is going directly to convey how moduli areas of curves are developed, illustrates regular purposes with the proofs of the Brill-Noether and Gieseker-Petri theorems through restrict linear sequence, and surveys crucial effects approximately their geometry starting from irreducibility and entire subvarieties to plentiful divisors and Kodaira size. With over a hundred and eighty routines and 70 figures, the e-book additionally presents a concise creation to the most effects and open difficulties approximately very important themes which aren't coated intimately.

Show description

Read Online or Download Moduli of Curves (Graduate Texts in Mathematics) PDF

Best Algebraic Geometry books

Fractured Fractals and Broken Dreams: Self-Similar Geometry through Metric and Measure (Oxford Lecture Series in Mathematics and Its Applications)

Fractal styles have emerged in lots of contexts, yet what precisely is a trend? How can one make certain the buildings mendacity inside items and the relationships among them? This publication proposes new notions of coherent geometric constitution to supply a clean method of this frequent box. It develops a brand new idea of self-similarity referred to as "BPI" or "big items of itself," which makes the sphere a lot more straightforward for individuals to go into.

The Arithmetic of Elliptic Curves (Graduate Texts in Mathematics)

The idea of elliptic curves is distinctive through its lengthy background and via the range of the tools which were utilized in its learn. This publication treats the mathematics process in its smooth formula, by using uncomplicated algebraic quantity concept and algebraic geometry. Following a short dialogue of the mandatory algebro-geometric effects, the ebook proceeds with an exposition of the geometry and the formal staff of elliptic curves, elliptic curves over finite fields, the advanced numbers, neighborhood fields, and international fields.

A First Course in Modular Forms (Graduate Texts in Mathematics, Vol. 228)

This ebook introduces the speculation of modular varieties, from which all rational elliptic curves come up, with an eye fixed towards the Modularity Theorem. dialogue covers elliptic curves as complicated tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner idea; Hecke eigenforms and their mathematics homes; the Jacobians of modular curves and the Abelian kinds linked to Hecke eigenforms.

Extra info for Moduli of Curves (Graduate Texts in Mathematics)

Show sample text content

Rated 4.42 of 5 – based on 27 votes