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The Kodaira dimension of Lefschetz fibrations
, 2008
"... In this note, we verify that the complex Kodaira dimension κ h equals the symplectic Kodaira dimension κ s for smooth 4−manifolds with complex and symplectic structures. We also calculate the Kodaira dimension for many Lefschetz fibrations. ..."
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Cited by 7 (3 self)
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In this note, we verify that the complex Kodaira dimension κ h equals the symplectic Kodaira dimension κ s for smooth 4−manifolds with complex and symplectic structures. We also calculate the Kodaira dimension for many Lefschetz fibrations.
Kodaira dimension and the Yamabe problem
 Comm. Anal. Geom
, 1999
"... The Yamabe invariant Y (M) of a smooth compact manifold is roughly the supremum of the scalar curvatures of unitvolume constantscalar curvature Riemannian metrics g on M. (To be absolutely precise, one only considers constantscalarcurvature metrics which are Yamabe minimizers, but this does not ..."
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Cited by 41 (4 self)
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not affect the sign of the answer.) If M is the underlying smooth 4manifold of a complex algebraic surface (M, J), it is shown that the sign of Y (M) is completely determined by the Kodaira dimension
Kodaira dimension and Symplectic Sums
"... Abstract. We show that smoothly nontrivial symplectic sums of symplectic 4manifolds along surfaces of positive genus are never rational or ruled, and we enumerate each case in which they have Kodaira dimension zero (i.e., are blowups of symplectic 4manifolds with torsion canonical class). In parti ..."
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Cited by 8 (0 self)
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Abstract. We show that smoothly nontrivial symplectic sums of symplectic 4manifolds along surfaces of positive genus are never rational or ruled, and we enumerate each case in which they have Kodaira dimension zero (i.e., are blowups of symplectic 4manifolds with torsion canonical class
SEMICONTINUITY OF KODAIRA DIMENSION
"... Let X be a compact analytic space (or a complete algebraic variety) and let L be a line bundle on X and denote by ft: X — • P ^ the rational map defined by the global sections of L®'. The Ldimension of X, K(X> L) is defined by K(X, L) = I ta(d im ( ƒ,(*)) I»oo with the convention K(X, L ..."
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(X, L) = ° ° if L has no nontrivial sections for all i "> 0. In the particular case when X is nonsingular and L = ^ is the canonical bundle, the invariant K(X) = K(X, £2) is called the canonical (or Kodaira) dimension of X and is the fundamental invariant in the classification of sur
Kodaira dimension of subvarieties
 Intl. J. Math
, 1999
"... In this article we study how the birational geometry of a normal projective variety X is influenced by a normal subvariety A ⊂ X. One of the most basic examples in this context is provided by the following situation. Let f: X → Y be a surjective ..."
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Cited by 9 (2 self)
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In this article we study how the birational geometry of a normal projective variety X is influenced by a normal subvariety A ⊂ X. One of the most basic examples in this context is provided by the following situation. Let f: X → Y be a surjective
On the logarithmic Kodaira dimension of affine threefolds
"... In the theory of affine varieties... In this article, we shall consider how to analyze smooth ane threefolds associated to the log Kodaira dimension and make the framework for this purpose under a certain geometric condition. As a consequence of our result, under this geometric condition, we can des ..."
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Cited by 3 (1 self)
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In the theory of affine varieties... In this article, we shall consider how to analyze smooth ane threefolds associated to the log Kodaira dimension and make the framework for this purpose under a certain geometric condition. As a consequence of our result, under this geometric condition, we can
KODAIRA DIMENSION OF SUBVARIETIES II
, 2005
"... 3. A criterion for uniruledness 2 4. Computing invariants 5 ..."
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Cited by 3 (0 self)
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3. A criterion for uniruledness 2 4. Computing invariants 5
KODAIRA DIMENSION OF SYMMETRIC POWERS
, 2000
"... We work over the complex numbers. When X is a smooth projective curve of genus g, elementary arguments show that the dth symmetric power S d X is uniruled as soon as d> g, and therefore that the plurigenera vanish. When the dimension of X is greater than one, the situation is quite different. Usi ..."
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Cited by 1 (0 self)
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We work over the complex numbers. When X is a smooth projective curve of genus g, elementary arguments show that the dth symmetric power S d X is uniruled as soon as d> g, and therefore that the plurigenera vanish. When the dimension of X is greater than one, the situation is quite different
Results 1  10
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213