Symplectic 4-manifolds with Kodaira dimension zero
نویسندگان
چکیده
منابع مشابه
Quaternionic Bundles and Betti Numbers of Symplectic 4-manifolds with Kodaira Dimension Zero
The Kodaira dimension of a non-minimal manifold is defined to be that of any of its minimal models. It is shown in [12] that, if ω is a Kähler form on a complex surface (M,J), then κ(M,ω) agrees with the usual holomorphic Kodaira dimension of (M,J). It is also shown in [12] that minimal symplectic 4−manifolds with κ = 0 are exactly those with torsion canonical class, thus can be viewed as sympl...
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Modulo trivial exceptions, we show that symplectic sums of symplectic 4-manifolds 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 4-manifolds with torsion canonical class). In particular, a symplectic four-manifold of Kodaira dimension zero arises by such a surgery only if it is d...
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Motivated by the above problems, we now turn to the results of this paper. We first look at the case when A is an abelian variety and φ : A → A is an endomorphism satisfying a mild polarization hypothesis. In this setting we are able to prove that #Fix(φl) grows exponentially as a function of l. More preciesely, let Ai be a simple abelian subvariety of A of dimension gi for i = 1, . . . ,m. Sup...
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 2006
ISSN: 0022-040X
DOI: 10.4310/jdg/1175266207