Algebraic Geometry

Download E-books 3264 and All That: A Second Course in Algebraic Geometry PDF

This e-book can shape the foundation of a moment path in algebraic geometry. As motivation, it takes concrete questions from enumerative geometry and intersection thought, and gives instinct and procedure, in order that the scholar develops the power to resolve geometric difficulties. The authors clarify key principles, together with rational equivalence, Chow jewelry, Schubert calculus and Chern periods, and readers will take pleasure in the plentiful examples, many supplied as routines with suggestions on hand on-line. Intersection is anxious with the enumeration of options of structures of polynomial equations in different variables. it's been an lively sector of arithmetic because the paintings of Leibniz. Chasles' nineteenth-century calculation that there are 3264 delicate conic aircraft curves tangent to 5 given common conics used to be a massive landmark, and was once the muse at the back of the identify of this booklet. Such computations have been motivation for Poincaré's improvement of topology, and for plenty of next theories, in order that intersection concept is now a vital subject of contemporary arithmetic.

Show description

Read or Download 3264 and All That: A Second Course in Algebraic Geometry PDF

Similar 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 development? How can one make exact the constructions mendacity inside of items and the relationships among them? This ebook proposes new notions of coherent geometric constitution to supply a clean method of this established box. It develops a brand new proposal of self-similarity known as "BPI" or "big items of itself," which makes the sphere a lot more uncomplicated for individuals to go into.

The Arithmetic of Elliptic Curves (Graduate Texts in Mathematics)

The speculation of elliptic curves is wonderful via its lengthy background and by way of the range of the tools which have been utilized in its examine. This e-book treats the mathematics process in its sleek formula, by utilizing simple algebraic quantity idea and algebraic geometry. Following a quick 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 publication 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 advanced tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner thought; Hecke eigenforms and their mathematics homes; the Jacobians of modular curves and the Abelian forms linked to Hecke eigenforms.

Additional info for 3264 and All That: A Second Course in Algebraic Geometry

Show sample text content

Rated 4.58 of 5 – based on 3 votes