By Qing Liu,Reinie Erne
The first half introduces uncomplicated gadgets corresponding to schemes, morphisms, base swap, neighborhood houses (normality, regularity, Zariski's major Theorem). this is often by means of 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 conception. the 1st half ends with the concept of Riemann-Roch and its software to the examine of soft projective curves over a field.
Singular curves are taken care of via a close learn of the Picard group.
The moment half begins with blowing-ups and desingularisation (embedded or no longer) of fibered surfaces over a Dedekind ring that leads directly to intersection conception on mathematics surfaces. Castelnuovo's criterion is proved and likewise the lifestyles of the minimum standard version. This results in the research of aid of algebraic curves. The case of elliptic curves is studied intimately. The ebook concludes with the funadmental theorem of strong relief of Deligne-Mumford.
The e-book is basically self-contained, together with the mandatory fabric on commutative algebra. the necessities are for that reason few, and the e-book may still go well with a graduate pupil. It comprises many examples and approximately six hundred exercises.
Read or Download Algebraic Geometry and Arithmetic Curves (Oxford Graduate Texts in Mathematics (0-19-961947-6)) PDF
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