New PDF release: Abelian Coverings of the Complex Projective Plane Branched

By Eriko Hironaka

ISBN-10: 082182564X

ISBN-13: 9780821825648

This paintings reviews abelian branched coverings of soft complicated projective surfaces from the topological standpoint. Geometric information regarding the coverings (such because the first Betti numbers of a delicate version or intersections of embedded curves) is expounded to topological and combinatorial information regarding the bottom house and department locus. certain awareness is given to examples within which the bottom house is the complicated projective aircraft and the department locus is a configuration of strains.

Show description

Read or Download Abelian Coverings of the Complex Projective Plane Branched Along Configurations of Real Lines PDF

Similar science & mathematics books

International Mathematical Olympiads, 1959-1977 - download pdf or read online

The overseas Olympiad has been held each year seeing that 1959; the U. S. started partaking in 1974, whilst the 16th foreign Olympiad was once held in Erfurt, G. D. R. In 1974 and 1975, the nationwide technological know-how starting place funded a 3 week summer time work out with Samuel L. Greitzer of Rutgers college and Murray Klamkin of the college of Alberta because the U.

Download e-book for kindle: Nonlinear programming by Peter Zörnig

This e-book is an advent to nonlinear programming, written for college students from the fields of utilized arithmetic, engineering, and economic system. It offers with theoretical foundations to boot assolution equipment, starting with the classical methods and achieving as much as "modern" equipment. numerous examples, routines with specific strategies and purposes are supplied, making the textual content sufficient for person experiences

Additional info for Abelian Coverings of the Complex Projective Plane Branched Along Configurations of Real Lines

Example text

Proof. Define L' to be the lift of L containing the edge f'(e\). 6. • The rest follows We are now ready to find lifting data for a C lifting in p : X —• Y. 9 PROPOSITION. For each proper transform L G C of a line L in C, let V be the curve in p w l (L) corresponding to V under the birational map ? : X —• X. For each point p ETy let E'p be the curve in p~l(Ep) mapping to f'(p) under ?. Let $ : J-+G be defined by V(q,L) = ^(cr(g),L) for all lines L in C and let $ ( £ p ) be the identity element. Then ^ is lifting data for the liftings.

Jv > be a presentation for 7Ti(P2 — C). Let A be the matrix of Fox derivatives 2(dRi\ dfij The matrix A is called the Alexander matrix for the presentation. 5), p. 5 PROPOSITION. The Alexander matrix A is a presentation matrix for the first homology group Ui(Xu1F;Z) considered as a Z[G]-module, for F any fiber. D, Computing b\. Let Clk be the set of ^-tuples of nth roots of unity and, for each element w = (u>i,... ,o>p) in Q,-£, let rw :Z[G]-*Z[fi n ] be the Z-module homomorphism defined by Tu,(0,-)=Wt, where Qi = <^(/i»).

Hirz], p. 122) Hirzebruch coverings X are smooth. We give a proof in Remark III. 6 using the language developed in Chapter I. In the process we show how to find the generators of the stabilizer and inertia subgroups of the branch locus of p and p. 4 that, if : Hi(P 2 - £ ; Z ) -+ H X (P 2 - £ ; Z / n Z) is the defining map of the covering, to each line L in £ there is a canonically associated element HL € Hi(P 2 — £ ; Z ) which can be realized as a positively oriented meridianal loop around L.

Download PDF sample

Abelian Coverings of the Complex Projective Plane Branched Along Configurations of Real Lines by Eriko Hironaka


by Jeff
4.5

Rated 4.88 of 5 – based on 6 votes