منابع مشابه
Lefschetz Fibrations in Symplectic Geometry
One of the cornerstones of complex geometry is the link between positivity of curvature and ampleness. Let X be a compact complex manifold and L ! X be a holomorphic line bundle over X. Suppose that L has a unitary connection whose curvature form is ?2i! where ! is a positive (1; 1)-form on X. Then for large k the line bundle L k has many holomorphic sections. More precisely, the holo-morphic s...
متن کاملLefschetz Fibrations and Symplectic Homology
We show that for each k > 3 there are infinitely many finite type Stein manifolds diffeomorphic to Euclidean space R which, as symplectic manifolds are pairwise not symplectomorphic to each other.
متن کاملSymplectic Lefschetz fibrations with arbitrary fundamental groups
In this paper we give an explicit construction of a symplectic Lefschetz fibration whose total space is a smooth compact four dimensional manifold with a prescribed fundamental group. We also study the numerical properties of the sections in symplectic Lefschetz fibrations and their relation to the structure of the monodromy group. Partially supported by DGYCYT grant PB96-0234 Partially support...
متن کاملSymplectic Lefschetz Fibrations on S ×m
A remarkable theorem of Donaldson [D] says that a symplectic 4manifold admits a Lefschetz pencil by symplectic surfaces. Given a Lefschetz pencil on a 4-manifold X, one can blow up points at the base locus to get a Lefschetz fibration of X over S, which admits a nice handlebody decomposition and can be described by geometric monodromy representation into the mapping class group of a regular fib...
متن کاملSymplectic Lefschetz fibrations and the geography of symplectic 4-manifolds
This paper is a survey of results which have brought techniques from the theory of complex surfaces to bear on symplectic 4-manifolds. Lefschetz fibrations are defined and some basic examples from complex surfaces discussed. Two results on the relationship between admitting a symplectic structure and admitting a Lefschetz fibration are explained. We also review the question of geography: which ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Geometry & Topology
سال: 2000
ISSN: 1364-0380,1465-3060
DOI: 10.2140/gt.2000.4.517