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34.97

By Qing Liu,Reinie Erne

This e-book is a basic creation to the speculation of schemes, by means of purposes to mathematics surfaces and to the speculation of relief of algebraic curves.

The first half introduces uncomplicated items akin to schemes, morphisms, base switch, neighborhood homes (normality, regularity, Zariski's major Theorem). this can be through the extra international 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 idea. the 1st half ends with the theory of Riemann-Roch and its software to the learn of delicate projective curves over a field.
Singular curves are taken care of via an in depth research 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 concept on mathematics surfaces. Castelnuovo's criterion is proved and likewise the life of the minimum commonplace version. This ends up in the learn of aid of algebraic curves. The case of elliptic curves is studied intimately. The e-book concludes with the funadmental theorem of strong aid of Deligne-Mumford.

The publication is largely self-contained, together with the mandatory fabric on commutative algebra. the must haves are consequently few, and the booklet may still swimsuit 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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