Legendrian realization in convex Lefschetz fibrations and convex stabilizations
نویسندگان
چکیده
منابع مشابه
Legendrian Realization in Convex Lefschetz Fibrations and Convex Stabilizations
In this paper, we study compact convex Lefschetz fibrations on compact convex symplectic manifolds (i.e., Liouville domains) of dimension 2n + 2 which are introduced by Seidel and later also studied by McLean. By a result of Akbulut-Arikan, the open book on ∂W , which we call convex open book, induced by a compact convex Lefschetz fibration on W carries the contact structure induced by the conv...
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We show that if a contact open book (Σ, h) on a (2n+1)-manifoldM (n ≥ 1) is induced by a Lefschetz fibration π : W → D, then there is a one-to-one correspondence between positive stabilizations of (Σ, h) and positive stabilizations of π. More precisely, any positive stabilization of (Σ, h) is induced by the corresponding positive stabilization of π, and conversely any positive stabilization of ...
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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...
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ژورنال
عنوان ژورنال: Forum Mathematicum
سال: 2015
ISSN: 0933-7741,1435-5337
DOI: 10.1515/forum-2013-6009