Get Complex Algebraic Surfaces PDF

By Arnaud Beauville

ISBN-10: 0521495105

ISBN-13: 9780521495103

The class of algebraic surfaces is an problematic and engaging department of arithmetic, built over greater than a century and nonetheless an lively zone of study at the present time. during this publication, Professor Beauville offers a lucid and concise account of the topic, expressed easily within the language of contemporary topology and sheaf thought, and obtainable to any budding geometer. A bankruptcy on initial fabric guarantees that this quantity is self-contained whereas the routines prevail either in giving the flavour of the classical topic, and in equipping the reader with the recommendations wanted for examine. The e-book is geared toward graduate scholars in geometry and topology.

Show description

Read or Download Complex Algebraic Surfaces PDF

Best algebraic geometry books

Download e-book for kindle: An Introduction to Riemann Surfaces, Algebraic Curves and by Martin Schlichenmaier

This ebook supplies an creation to fashionable geometry. ranging from an ordinary point the writer develops deep geometrical recommendations, enjoying an enormous position these days in modern theoretical physics. He provides quite a few innovations and viewpoints, thereby displaying the relatives among the choice methods.

Workshop on Algebraic Geometry and Geome, Rimvydas's Topics in algebraic geometry and geometric modeling: PDF

Surveys, tutorials, and study papers from a summer time 2002 workshop study a number of subject matters in algebraic geometry and geometric modeling. Papers are divided into sections on modeling curves and surfaces, multisided patches, implicitization and parametrization, subject types, and combined quantity and resultants, and papers from either disciplines are integrated in each one part.

Download PDF by Jorg Jahnel: Brauer groups, Tamagawa measures, and rational points on

The imperative subject of this ebook is the research of rational issues on algebraic sorts of Fano and intermediate type--both by way of while such issues exist and, in the event that they do, their quantitative density. The booklet includes 3 elements. within the first half, the writer discusses the idea that of a top and formulates Manin's conjecture at the asymptotics of rational issues on Fano types.

Additional resources for Complex Algebraic Surfaces

Sample text

Let Lit = (pi, pj) for i # j. (a) We want to show that this linear system separates points on P6. So let x, y E P6 with x # y. Choose i with pi $ e(x), e(y) and fl - = {x} for pk 0 {pi, pj, e(x)}. Hence x 0 Q. Then y E Q for at most one value of j. On the other, hand, y E Lij for at most one j; thus there is a j such that the cubic Q U Lii passes through x but not y. Hence the morphism j : P6 --+ IEn3 is injective. (b) Let x E P2 - {PI, ... , P6}. The cubits Qi U (pi, x) do not all have the same tangent at x, so that j is an immersion at x.

18 Let S = ]PC(E) be a geometrically ruled surface over C, p : S --* C the structure map. Write h for the class of the sheaf Os(l) in PicS (or in H2(S,7L)). Then (i) Pic S = p* Pic C ®7Lh. (ii) H2(S,7L) = 7Lh ® 7Lf, where f is the class of a fibre. (iii) h2 = deg(E). (iv) [K] = -2h + (deg(E) + 2g(C) - 2) f in H2(S, Z). Proof First we prove (i). F = 0; so it is enough to prove that D is the pull-back of a divisor on C. K - 2n, and h°(K - Dn) = 0 whenever n is sufficiently large. , so that the system ID,, I is non-empty for sufficiently large n.

Show that V is the set of conics of rank 1 in P (use (5)(a)). Deduce that V is the intersection of 5 quadrics in Q. Show that the union of the bisecants of V is the set X of singular conics in P. Deduce that X is a cubic hypersurface in (Q whose singular locus is V. (6) Let f : 1112 -> I(1s be the morphism corresponding to a 3-dimensional base-point free linear system of conics. Let R be the dual pencil of conics in ](D2; suppose that R contains 3 distinct singular conics, each of rank 2. These correspond to 3 pairs of points (pi, p;), i = 1, 2, 3.

Download PDF sample

Complex Algebraic Surfaces by Arnaud Beauville


by Ronald
4.2

Rated 4.89 of 5 – based on 34 votes