By Qing Liu,Reinie Erne
The first half introduces simple items equivalent to schemes, morphisms, base switch, neighborhood houses (normality, regularity, Zariski's major Theorem). this is often by way of 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 concept. the 1st half ends with the theory of Riemann-Roch and its program to the learn of soft projective curves over a field.
Singular curves are taken care of via a close learn of the Picard group.
The moment half starts off with blowing-ups and desingularisation (embedded or no longer) of fibered surfaces over a Dedekind ring that leads directly to intersection concept on mathematics surfaces. Castelnuovo's criterion is proved and likewise the lifestyles of the minimum average version. This ends up in the examine of aid of algebraic curves. The case of elliptic curves is studied intimately. The booklet concludes with the funadmental theorem of strong relief of Deligne-Mumford.
The ebook is basically self-contained, together with the mandatory fabric on commutative algebra. the must haves are for that reason few, and the ebook may still swimsuit a graduate scholar. 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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Algebraic Geometry and Arithmetic Curves (Oxford Graduate Texts in Mathematics (0-19-961947-6)) by Qing Liu,Reinie Erne