Download e-book for kindle: Algebraic Geometry and Arithmetic Curves (Oxford Graduate by Qing Liu,Reinie Erne

By Qing Liu,Reinie Erne

This publication is a common creation to the speculation of schemes, via purposes to mathematics surfaces and to the speculation of relief of algebraic curves.

The first half introduces easy items comparable to schemes, morphisms, base swap, neighborhood homes (normality, regularity, Zariski's major Theorem). this is often through the extra worldwide point: 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 conception. the 1st half ends with the concept of Riemann-Roch and its program to the research of soft projective curves over a field.
Singular curves are taken care of via an in depth examine of the Picard group.

The moment half starts off with blowing-ups and desingularisation (embedded or now not) of fibered surfaces over a Dedekind ring that leads directly to intersection conception on mathematics surfaces. Castelnuovo's criterion is proved and in addition the life of the minimum common version. This results in the examine of relief of algebraic curves. The case of elliptic curves is studied intimately. The ebook concludes with the funadmental theorem of sturdy aid of Deligne-Mumford.

The e-book is basically self-contained, together with the mandatory fabric on commutative algebra. the necessities are accordingly few, and the ebook may still go well with a graduate scholar. It comprises many examples and approximately six hundred exercises.

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Algebraic Geometry and Arithmetic Curves (Oxford Graduate Texts in Mathematics (0-19-961947-6)) by Qing Liu,Reinie Erne

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