منابع مشابه
Hamiltonian S1-manifolds Are Uniruled
The main result of this note is that every closed Hamiltonian S manifold is uniruled, i.e. it has a nonzero Gromov–Witten invariant one of whose constraints is a point. The proof uses the Seidel representation of π1 of the Hamiltonian group in the small quantum homology of M as well as the blow up technique recently introduced by Hu, Li and Ruan. It applies more generally to manifolds that have...
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In an earlier paper we explained how to convert the problem of symplectically embedding one 4-dimensional ellipsoid into another into the problem of embedding a certain set of disjoint balls into CP 2 by using a new way to desingularize orbifold blow ups Z of the weighted projective space CP 2 1,m,n. We now use a related method to construct symplectomorphisms of these spaces Z. This allows us t...
متن کاملOn Varieties Which Are Uniruled by Lines
Using the ♯-minimal model program of uniruled varieties we show that for any pair (X,H) consisting of a reduced and irreducible variety X of dimension k ≥ 3 and a globally generated big line bundle H on X with d := H and n := h(X,H) − 1 such that d < 2(n− k)− 4, then X is uniruled of H-degree one, except if (k, d, n) = (3, 27, 19) and a ♯-minimal model of (X,H) is (P3,OP3(3)). We also show that...
متن کاملPerturbed S1-symmetric hamiltonian systems
Keywords--Pala is-Smale condition, Critical point theory, Hamiltonian systems, Perturbation from symmetry, Multiple periodic solutions. 1. I N T R O D U C T I O N In this paper, in the spirit of [1], we want to investigate the effect of perturbing the S l symmet ry of a general class of Hamiltonian systems. Studied around 1980 by Bahri and Berestycki in [2], the problem of finding multiple peri...
متن کاملContact hypersurfaces in uniruled symplectic manifolds always separate
We observe that nonzero Gromov-Witten invariants with marked point constraints in a closed symplectic manifold imply restrictions on the homology classes that can be represented by contact hypersurfaces. As a special case, contact hypersurfaces must always separate if the symplectic manifold is uniruled. This removes a superfluous assumption in a result of G. Lu [Lu00], thus implying that all c...
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2009
ISSN: 0012-7094
DOI: 10.1215/00127094-2009-003