Download Analytic Methods in Algebraic Geometry by Jean-Pierre Demailly PDF

By Jean-Pierre Demailly

This quantity is a spread of lectures given by way of the writer on the Park urban arithmetic Institute (Utah) in 2008, and on different events. the aim of this quantity is to explain analytic innovations important within the examine of questions referring to linear sequence, multiplier beliefs, and vanishing theorems for algebraic vector bundles. the writer goals to be concise in his exposition, assuming that the reader is already a bit conversant in the fundamental thoughts of sheaf idea, homological algebra, and intricate differential geometry. within the ultimate chapters, a few very contemporary questions and open difficulties are addressed--such as effects concerning the finiteness of the canonical ring and the abundance conjecture, and effects describing the geometric constitution of Kahler types and their optimistic cones.

Show description

Read or Download Analytic Methods in Algebraic Geometry PDF

Best algebraic geometry books

Advanced Topics in the Arithmetic of Elliptic Curves

Within the mathematics of Elliptic Curves, the writer provided the elemental concept culminating in basic worldwide effects, the Mordell-Weil theorem at the finite new release of the gang of rational issues and Siegel's theorem at the finiteness of the set of necessary issues. This booklet keeps the learn of elliptic curves by way of providing six vital, yet a little bit extra really good subject matters: I.

Galois Cohomology

This quantity is an English translation of "Cohomologie Galoisienne" . the unique variation (Springer LN5, 1964) was once in accordance with the notes, written with the aid of Michel Raynaud, of a direction I gave on the collage de France in 1962-1963. within the current variation there are many additions and one suppression: Verdier's textual content at the duality of profinite teams.

Birationally Rigid Varieties: Mathematical Analysis and Asymptotics

Birational tension is a amazing and mysterious phenomenon in higher-dimensional algebraic geometry. It seems that sure ordinary households of algebraic forms (for instance, 3-dimensional quartics) belong to an analogous category variety because the projective area yet have significantly various birational geometric houses.

Extra info for Analytic Methods in Algebraic Geometry

Sample text

5 Poincare groups 41 (7) - The homomorphism Hn(G, I) ---t QpjZp is an isomorphism. The group of Z-endomorphisms of I is isomorphic to Zp (acting in an obvious way). Since these actions commute with the action of G, we see that HomG(I,I) = Zp. But, HomG(I,I) is also equal to the dual of Hn(G,I), cf. 5. Therefore we have a canonical isomorphism Hn(G,I) ---t QpjZp, and it is not difficult to see that it is the homomorphism i. (8) - End of the proof There remains part (c), i. e. the duality between Hi(G, A) and Hn-i(G, A).

G,G), where (G,G) denotes the closure of the commutator subgroup of G. The groups GjG* and HI(G) are each other's duals (the first being compact and the second discrete). Prop. §4 Cohomology of pro-p-groups Proposition 23 bis. In order that a morphism G1 -+ G2 be surjective, it is necessary and sufficient that the same be true o/the morphism Gl/Gi -+ G 2 IG'2 which it induces. Thus, G* plays the role of a "radical", and the proposition is analogous to "Nakayama's lemma", so useful in commutative algebra.

The following proposition refines prop. 15: Proposition 22. Let G be a profinite group and H a closed normal subgroup of G. Assume that n = cdp(H) and that m = cdp(Gj H) are finite. One has the equality cdp(G) =n+m in each of the following two cases: (i) H is a pro-p-group and Hn(H, ZjpZ) is finite. (ii) H is contained in the center of G. Let (GjH)' be a Sylow p-subgroup of GjH, and let G' be its inverse image in G. One knows that cdp(G') ::; cdp(G) ::; n + m, and that cdp(G'jH) = m. It is then sufficient to prove that cdp(G') = n + m, in other words one may assume that GjH is a pro-p-group.

Download PDF sample

Rated 4.32 of 5 – based on 21 votes