Algebraic Geometry. Proc. conf. Sitges (Barcelona), 1983 by Eduard Casas-Alvero, Gerald E. Welters, Sebastian PDF

By Eduard Casas-Alvero, Gerald E. Welters, Sebastian Xambo-Descamps

ISBN-10: 3540152326

ISBN-13: 9783540152323

Show description

Read Online or Download Algebraic Geometry. Proc. conf. Sitges (Barcelona), 1983 PDF

Similar geometry and topology books

Nonpositive curvature: geometric and analytic aspects - download pdf or read online

Discusses a variety of geometric and analytic features of non-positive curvature, beginning with Riemannian examples and pressure theorems. Treats generalized notions of nonpositive curvature within the feel of Alexandrov and Busemann & the idea of harmonic maps with values in such areas. Paper.

Extra info for Algebraic Geometry. Proc. conf. Sitges (Barcelona), 1983

Example text

It is now easy to verify that the arrows ( B , g , B , Uf Y ) and (Y,f,Bg Uf Y ) satisfy the universal property; the space B, Uf Y (or any space homeomorphic to it) is the pushout space of f and g. A case of particular importance is when g is the inclusion of a closed subspace A into Y : then, we denote g by i : A + Y and the pushout space just by B Uf Y ; the space B Uf Y is the adjuntion of Y to B via f. The map f:Y+BufY obtained in the construction of the adjunction space B Uf Y and - in view of the universal property for pushouts - the compositions of f with any homeomorphism B Uf Y 2 2 are called characteristic maps of the adjunction.

The following statements are equivalent: 1) for any two given maps f : X x ( 0 ) -+ Z and G : A x I -+ Z which coincide when restricted to A x ( 0 ) there is a map F : X x I -+ Z such that F restricted to X x (0) is f and F restricted to A x I is G; 2) the space X = X x (0) U A x I is a retract of X x I ; 3) X is a strong deformation retract of X x I . 3. COFIBRATIONS 51 io denotes the inclusion of (0) into I . Then X x I is a weak pushout of these two arrows 2 is a retract of X x I . 2) j 3): Let T : X x I +X be a retraction; for every (2,t ) E X X I , write and notice that r,y(z,O) = z , r ~ ( z , O= ) 0 for every z E X and, for every a E A , ~ .

For every a : I -+ B such that a(0) = b, there exists a unique path a' : I + E such that a'(0) = e, and pa' = a. 1 Proof - Let U be an open covering of B satisfying the condition spelled out in the definition of covering map. Using the Lebesgue number of the covering a-'(U) of I , we can construct a subdivision 0 = t,, < tl < t 2 < ... 4, for every i = 0, ,n. Set a'(0) = e, and suppose that we have defined a' for every t E Assume [0, t i ] ;we are going to define a' in the closed interval [ti, -- that a([ti,tj+l]) c U E U and that p-'(U) is the disjoint union of the open sets V, of E , indexed by a set A.

Download PDF sample

Algebraic Geometry. Proc. conf. Sitges (Barcelona), 1983 by Eduard Casas-Alvero, Gerald E. Welters, Sebastian Xambo-Descamps


by John
4.5

Rated 4.45 of 5 – based on 10 votes