An Invitation to Web Geometry - download pdf or read online
By Jorge Vitório Pereira, Luc Pirio
This publication takes an in-depth examine abelian family of codimension one webs within the advanced analytic surroundings. In its classical shape, internet geometry is composed within the learn of webs as much as neighborhood diffeomorphisms. an important a part of the speculation revolves round the inspiration of abelian relation, a selected type of useful relation one of the first integrals of the foliations of an internet. major focuses of the e-book comprise what number abelian kin can an online hold and which webs are sporting the maximal attainable variety of abelian family. The ebook bargains whole proofs of either Chern’s certain and Trépreau’s algebraization theorem, together with all of the precious must haves that transcend user-friendly complicated research or uncomplicated algebraic geometry. lots of the examples identified modern of non-algebraizable planar webs of maximal rank are mentioned intimately. A old account of the algebraization challenge for maximal rank webs of codimension one can also be presented.
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Additional info for An Invitation to Web Geometry
W/. W 0 / ! Á0i /kiD1 7 ! W/ is an analytic invariant attached to W. We will prove below in Sect. n 1/ 1 : j D1 The space of abelian relations of a global web is no longer a vector space but a local system defined on an open subset containing the complement of the discriminant of the web. This can be inferred from the results by Pantazi–Hénaut expounded in Sect. 3 of Chap. 6. 2]. Note that both the approaches mentioned above deal a priori with webs on surfaces, but deducing the general case from them can be done without any real difficulty.
For an elementary proof and a comprehensive account on Chasles’ Theorem including its distinguished lineage and recent—rather non-elementary—developments, the reader is urged to consult . `0 /. To choose a point x1 2 L1 is therefore the same as choosing a line through p1 2 C1 PL 2 . If such a line is sufficiently close to `0 , then it cuts C3 in a unique point still denoted x1 . In this way the leaf L1 of F1 can be identified with the curve C3 . It will also be useful to identify through the same process L2 , the leaf of F2 through `0 2 PL 2 , with C1 and L3 with C2 (Fig.
This implies that GL contains a transposition. Proving that GL is normal requires more technical arguments and will not be treated here. 3 in  more specifically). 3, this yields GL D Sk for L generic, which implies in turn that the monodromy group of WC is the full symmetric group. 5 in  for details. 5. Let C be an irreducible non-degenerate projective curve in Pn , n 2. H / is a germ of smooth web. By duality, the proposition is clearly equivalent to the so-called uniform position principle for curves.
An Invitation to Web Geometry by Jorge Vitório Pereira, Luc Pirio