By David Mumford

From the experiences: "Although a number of textbooks on smooth algebraic geometry were released meanwhile, Mumford's "Volume I" is, including its predecessor the pink e-book of types and schemes, now as prior to some of the most very good and profound primers of recent algebraic geometry. either books are only actual classics!" Zentralblatt

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 targeted the constructions mendacity inside of gadgets and the relationships among them? This booklet proposes new notions of coherent geometric constitution to supply a clean method of this standard box. It develops a brand new idea of self-similarity referred to as "BPI" or "big items of itself," which makes the sector a lot more straightforward for individuals to go into.

The Arithmetic of Elliptic Curves (Graduate Texts in Mathematics)

The idea of elliptic curves is unusual by means of its lengthy historical past and through the range of the equipment which have been utilized in its learn. This booklet treats the mathematics procedure in its smooth formula, by using easy algebraic quantity thought and algebraic geometry. Following a quick dialogue of the mandatory algebro-geometric effects, the booklet proceeds with an exposition of the geometry and the formal staff of elliptic curves, elliptic curves over finite fields, the complicated numbers, neighborhood fields, and worldwide fields.

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

This ebook introduces the idea of modular kinds, from which all rational elliptic curves come up, with a watch 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 conception; Hecke eigenforms and their mathematics homes; the Jacobians of modular curves and the Abelian types linked to Hecke eigenforms.

Extra resources for Algebraic Geometry I: Complex Projective Varieties

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