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14
GromovWitten invariants and pseudo symplectic capacities
, 2001
"... We define the concept of pseudo symplectic capacities that is a mild generalization of that of the symplectic capacities. In particular a typical pseudo symplectic capacity, whose special case is a variant of the HoferZehnder symplectic capacity, is constructed and estimated in terms of the Gromov ..."
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Cited by 24 (7 self)
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We define the concept of pseudo symplectic capacities that is a mild generalization of that of the symplectic capacities. In particular a typical pseudo symplectic capacity, whose special case is a variant of the HoferZehnder symplectic capacity, is constructed and estimated in terms of the GromovWitten invariants. An example is also given to illustrate that using the pseudo symplectic capacity may get better estimation result than doing the HoferZehnder capacity. Among various potential applications of these estimations three typical applications are given. The first one is to derive some general nonsqueezing theorems that generalize and unite many past versions. The second is to give an alternate generalization of LalondeMcDuff theorem on length minimizing Hamiltonian paths to a general closed symplectic manifold. In the third application we give the new symplectic packing obstructions for a wider class of symplectic manifolds.
Height zeta functions of toric varieties
, 1996
"... 2. Algebraic tori................................................ 6 ..."
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Cited by 17 (0 self)
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2. Algebraic tori................................................ 6
BIRATIONAL COBORDISM INVARIANCE OF UNIRULED SYMPLECTIC MANIFOLDS
, 2006
"... 2. Birational cobordism 3 2.1. Coupling form and linear deformations 4 2.2. Blowup and blowdown 6 ..."
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Cited by 15 (1 self)
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2. Birational cobordism 3 2.1. Coupling form and linear deformations 4 2.2. Blowup and blowdown 6
Hyperelliptic and trigonal Fano threefolds
, 2004
"... We classify Fano 3folds with canonical Gorenstein singularities whose anticanonical linear system has no base points but does not give an embedding, and we classify anticanonically embedded Fano 3folds with canonical Gorenstein singularities which are not an intersection of quadrics. ..."
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Cited by 6 (0 self)
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We classify Fano 3folds with canonical Gorenstein singularities whose anticanonical linear system has no base points but does not give an embedding, and we classify anticanonically embedded Fano 3folds with canonical Gorenstein singularities which are not an intersection of quadrics.
Birationally superrigid cyclic triple spaces
 Izv. Math
"... Abstract. We prove the birational superrigidity and the nonrationality of a cyclic triple cover of P 2n branched over a nodal hypersurface of degree 3n for n ≥ 2. In particular, the obtained result solves the problem of the birational superrigidity of smooth cyclic triple spaces. We also consider ce ..."
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Cited by 5 (3 self)
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Abstract. We prove the birational superrigidity and the nonrationality of a cyclic triple cover of P 2n branched over a nodal hypersurface of degree 3n for n ≥ 2. In particular, the obtained result solves the problem of the birational superrigidity of smooth cyclic triple spaces. We also consider certain relevant problems. 1. Introduction. The problem of the rationality of an algebraic variety 1 is one of the most interesting problems in algebraic geometry. Global holomorphic differential forms are natural birational invariants of a smooth algebraic variety that solve the problem ot the rationality of algebraic curves and surfaces (see [205], [100]). However, even in threedimensional
NONRATIONAL DEL PEZZO FIBRATIONS
, 2007
"... Abstract. Let X be a general divisor in 3M + nL  on the rational scroll Proj( ⊕ 4 i=1O P 1(di)), where di and n are integers, M is the tautological line bundle, L is a fibre of the natural projection to P 1, and d1 � · · · � d4 = 0. We prove that X is rational ⇐ ⇒ d1 = 0 and n = 1. 1. Introduc ..."
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Cited by 4 (1 self)
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Abstract. Let X be a general divisor in 3M + nL  on the rational scroll Proj( ⊕ 4 i=1O P 1(di)), where di and n are integers, M is the tautological line bundle, L is a fibre of the natural projection to P 1, and d1 � · · · � d4 = 0. We prove that X is rational ⇐ ⇒ d1 = 0 and n = 1. 1. Introduction. The rationality problem for threefolds 1 splits in three cases: conic bundles, del Pezzo fibrations, and Fano threefolds. The cases of conic bundles and Fano threefolds are well studied. Let ψ: X → P 1 be a fibration into del Pezzo surfaces of degree k � 1 such that X is smooth and rkPic(X) = 2. Then X is rational if k � 5. The following result is due to [1] and [12].
Topstable degenerations of finite dimensional representations I
"... Dedicated to Claus Michael Ringel on the occasion of his sixtieth birthday Abstract. Given a finite dimensional representation M of a finite dimensional algebra, two hierarchies of degenerations ofM are analyzed in the context of their natural orders: the poset of those degenerations ofM which share ..."
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Cited by 3 (1 self)
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Dedicated to Claus Michael Ringel on the occasion of his sixtieth birthday Abstract. Given a finite dimensional representation M of a finite dimensional algebra, two hierarchies of degenerations ofM are analyzed in the context of their natural orders: the poset of those degenerations ofM which share the topM/JM withM – here J denotes the radical of the algebra – and the subposet of those which share the full radical layering J lM/J l+1M l≥0 with M. In particular, the article addresses existence of proper topstable or layerstable degenerations – more generally, it addresses the sizes of the corresponding posets including bounds on the lengths of saturated chains – as well as structure and classification. 1.