Download E-books Algebraic Geometry and Arithmetic Curves (Oxford Graduate Texts in Mathematics) PDF

By Qing Liu

This new-in-paperback variation offers a normal creation to algebraic and mathematics geometry, beginning with the speculation of schemes, by means of functions to mathematics surfaces and to the idea of relief of algebraic curves.

The first half introduces easy items comparable to schemes, morphisms, base switch, neighborhood houses (normality, regularity, Zariski's major Theorem). this can be by way of the extra worldwide element: coherent sheaves and a finiteness theorem for his or her cohomology teams. Then follows a bankruptcy on sheaves of differentials, dualizing sheaves, and Grothendieck's duality idea. the 1st half ends with the theory of Riemann-Roch and its software to the examine of tender projective curves over a box. Singular curves are handled via an in depth research of the Picard group.

The moment half begins with blowing-ups and desingularization (embedded or no longer) of fibered surfaces over a Dedekind ring that leads directly to intersection thought on mathematics surfaces. Castelnuovo's criterion is proved and likewise the life of the minimum usual version. This ends up in the research of aid of algebraic curves. The case of elliptic curves is studied intimately. The ebook concludes with the basic theorem of strong aid of Deligne-Mumford.

This publication is basically self-contained, together with the mandatory fabric on commutative algebra. the must haves are few, and together with many examples and nearly six hundred routines, the publication is perfect for graduate students.

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