A Degree Doubling Formula for Braid Monodromies and Lefschetz Pencils
نویسنده
چکیده
Contents 1. Introduction 1 1.1. Braid monodromy invariants 3 1.2. The degree doubling process 6 1.3. Degree doubling for symplectic Lefschetz pencils 9 2. Stably quasiholomorphic coverings 10 2.1. Quasiholomorphic coverings and braided curves 10 2.2. Stably quasiholomorphic coverings 11 2.3. Proof of Proposition 1 18 3. The degree doubling formula for braid monodromies 21 3.
منابع مشابه
Lefschetz pencils and divisors in moduli space
We study Lefschetz pencils on symplectic four-manifolds via the associated spheres in the moduli spaces of curves, and in particular their intersections with certain natural divisors. An invariant defined from such intersection numbers can distinguish manifolds with torsion first Chern class. We prove that pencils of large degree always give spheres which behave “homologically” like rational cu...
متن کاملm at h . SG ] 2 1 O ct 2 00 2 GENERIC BEHAVIOR OF ASYMPTOTICALLY HOLOMORPHIC
We study some asymptotic properties of the sequences of symplectic Lefschetz pencils constructed by Donaldson. In particular we prove that the vanishing spheres of these pencils are, for large degree, conjugated under the action of the symplectomorphism group of the fiber. This implies the non-existence of homologically trivial vanishing spheres in these pencils. Moreover we show some basic top...
متن کاملThe Zariski-lefschetz Principle for Higher Homotopy Groups of Nongeneric Pencils
We prove a general Zariski-van Kampen-Lefschetz type theorem for higher homotopy groups of generic and nongeneric pencils on singular open complex spaces.
متن کاملBraid Monodromy of Special Curves
In this article, we compute the braid monodromy of two algebraic curves defined over R. These two curves are of complex level not bigger than 6, and they are unions of lines and conics. We use two different techniques for computing their braid monodromies. These results will be applied to computations of fundamental groups of their complements in C and CP.
متن کاملAppendix: Lefschetz Pencils with Imposed Subvarieties
In this appendix, which is entirely expository, we give some basic facts about the existence of Lefschetz pencils with imposed subvarieties. These facts are certainly well known to the experts, but we are unaware of a suitable reference. We thank de Caltaldo and Kollar for a very helpful conversation.
متن کامل