共查询到20条相似文献,搜索用时 31 毫秒
1.
We give effective bounds for the third Chern class of a semistable rank 2 reflexive sheaf on a canonically trivial threefold. 相似文献
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S. A. H. Cardona 《Annals of Global Analysis and Geometry》2013,44(4):455-469
We study the basic properties of Higgs sheaves over compact Kähler manifolds and establish some results concerning the notion of semistability; in particular, we show that any extension of semistable Higgs sheaves with equal slopes is semistable. Then, we use the flattening theorem to construct a regularization of any torsion-free Higgs sheaf and show that it is in fact a Higgs bundle. Using this, we prove that any Hermitian metric on a regularization of a torsion-free Higgs sheaf induces an admissible structure on the Higgs sheaf. Finally, using admissible structures we prove some properties of semistable Higgs sheaves. 相似文献
4.
N. A. Tyurin 《Theoretical and Mathematical Physics》2010,162(3):255-275
We introduce the notion of a pseudotoric structure on a symplectic manifold, generalizing the notion of a toric structure.
We show that such a pseudotoric structure can exist on toric and nontoric symplectic manifolds. For the toric manifolds, it
describes deformations of the standard toric Lagrangian fibrations; for the nontoric ones, it gives Lagrangian fibrations
with singularities that are very close to the toric fibrations. We present examples of toric manifolds with different pseudotoric
structures and prove that certain nontoric manifolds (smooth complex quadrics) have such structures. In the future, introducing
this new structure can be useful for generalizing the geometric quantization and mirror symmetry methods that work well in
the toric case to a broader class of Fano varieties. 相似文献
5.
Claudio Bartocci Ugo Bruzzo Daniel Hernndez Ruiprez Jos M. Muoz Porras 《Mathematische Nachrichten》2002,238(1):23-36
We consider a relative Fourier‐Mukai transform de.ned on elliptic fibrations over an arbitrary base scheme. This is used to construct relative Atiyah sheaves and generalize Atiyah and Tu's results about semistable sheaves over elliptic curves to the case of elliptic fibrations. Moreover we show that this transform preserves relative (semi)stability of sheaves of positive relative degree. 相似文献
6.
We investigate properties and describe examples of tilt-stable objects on a smooth complex projective threefold. We give a structure theorem on slope semistable sheaves of vanishing discriminant, and describe certain Chern classes for which every slope semistable sheaf yields a Bridgeland semistable object of maximal phase. Then, we study tilt stability as the polarization ω gets large, and give sufficient conditions for tilt-stability of sheaves of the following two forms: 1) twists of ideal sheaves or 2) torsion-free sheaves whose first Chern class is twice a minimum possible value. 相似文献
7.
Xiaolei LIU 《数学年刊B辑(英文版)》2016,37(6):875-890
The modular invariants of a family of curves are the degrees of the
pullback of the corresponding divisors by the moduli map. The
singularity indices were introduced by Xiao (1991) to classify
singular fibers of hyperelliptic fibrations and to compute global
invariants locally. In semistable case, the author shows that the
modular invariants corresponding to the boundary divisor classes are
just the singularity indices. As an application, the author shows
that the formula of Xiao for relative Chern numbers is the same as
that of Cornalba-Harris in semistable case. 相似文献
8.
John R. Klein 《manuscripta mathematica》1997,92(1):77-86
Using equivariant methods, we provide straightforward proofs of a result of Chachólski and a result of Spivak about fibrations. 相似文献
9.
We study global primary decompositions in the category of sheaves on a scheme which are equivariant under the action of an algebraic group. We show that equivariant primary decompositions exist if the group is connected. As main application we consider the case of varieties which are quotients of a quasi-affine variety by the action of a diagonalizable group and thus admit a homogeneous coordinate ring, such as toric varieties. Comparing these decompositions with primary decompositions of graded modules over the homogeneous coordinate ring, we show that these are equivalent if the action of the diagonalizable group is free. We give some specific examples for the case of toric varieties. 相似文献
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Takahiko Yoshida 《Advances in Mathematics》2011,227(5):1914
We introduce the notion of a local torus action modeled on the standard representation (for simplicity, we call it a local torus action). It is a generalization of a locally standard torus action and also an underlying structure of a locally toric Lagrangian fibration. For a local torus action, we define two invariants called a characteristic pair and an Euler class of the orbit map, and prove that local torus actions are classified topologically by them. As a corollary, we obtain a topological classification of locally standard torus actions, which includes the topological classifications of quasi-toric manifolds by Davis and Januszkiewicz and of effective T2-actions on four-dimensional manifolds without nontrivial finite stabilizers by Orlik and Raymond. We discuss locally toric Lagrangian fibrations from the viewpoint of local torus actions. We also investigate the topology of a manifold equipped with a local torus action when the Euler class of the orbit map vanishes. 相似文献
12.
For the action of a locally compact and totally disconnected group G on a pair of locally compact spaces X and Y we construct, by sheaf theoretic means, a new equivariant and bivariant cohomology theory. If we take for the first space Y an universal proper G-action then we obtain for the second space its delocalized equivariant homology. This is in exact formal analogy to the definition of equivariant K-homology by Baum, Connes, Higson starting from the bivariant equivariant Kasparov KK-theory. Under certain basic finiteness conditions on the first space Y we conjecture the existence of a Chern character from the equivariant Kasparov KK-theory of Y and X into our cohomology theory made two-periodic which becomes an isomorphism upon tensoring the KK-theory with the complex numbers. This conjecture is proved for profinite groups G. An essential role in our construction is played by a bivariant version of Segal localization which we establish for KK-theory. 相似文献
13.
Yongnam Lee 《Mathematische Nachrichten》2000,219(1):135-146
We classify the central fiber of a semistable degeneration (in the sense of the semistable reduction theorem) of Godeaux surfaces, under the condition that the dualizing sheaf is relativel nef. We prove in particular that if the central fiber is reducible then all its components have negative Kodaira dimension. As a corollary, this result provides a classification of possible central fibers of a semistable degeneration having two components. 相似文献
14.
Andreas Stieglitz 《manuscripta mathematica》1978,26(1-2):201-221
In this paper we study Grothendieck's equivariant sheaf cohomology H(X,G;G) for non-discrete topological groups G and G-sheavesG on a G-Space X. For compact groups and locally compact, totally disconnected groups we obtain detailed results relating H(X,G;-) to H(X;-)G and H(X/G;-). Furthermore we point out the connection between H(X,G;-) and Borel's equivariant cohomology HG(X;-). 相似文献
15.
Torus orbifolds are topological generalizations of symplectic toric orbifolds.The authours give a construction of smooth orbifolds with torus actions whose boundary is a disjoint union of torus orbifolds using a toric topological method. As a result, they show that any orientable locally standard torus orbifold is equivariantly cobordant to some copies of orbifold complex projective spaces. They also discuss some further equivariant cobordism results including the cases when torus orbifolds are actually torus manifolds. 相似文献
16.
In this note we show that the positivity property of the equivariant signature of the loop space, first observed in [MS1] in the case of the even-dimensional projective spaces, is valid for Picard number 2 toric varieties. A new formula for the equivariant signature of the loop space in the case of a toric spin variety is derived.Partially supported by an NSF grant 相似文献
17.
In this paper, we study semi-stable Higgs sheaves over compact Kähler manifolds. We prove that there is an admissible approximate Hermitian-Einstein structure on a semi-stable reflexive Higgs sheaf and consequently, the Bogomolov type inequality holds on a semi-stable reflexive Higgs sheaf. 相似文献
18.
Michael Wiemeler 《Mathematische Zeitschrift》2013,273(3-4):1063-1084
In 2006 Masuda and Suh asked if two compact non-singular toric varieties having isomorphic cohomology rings are homeomorphic. In the first part of this paper we discuss this question for topological generalizations of toric varieties, so-called torus manifolds. For example we show that there are homotopy equivalent torus manifolds which are not homeomorphic. Moreover, we characterize those groups which appear as the fundamental groups of locally standard torus manifolds. In the second part we give a classification of quasitoric manifolds and certain six-dimensional torus manifolds up to equivariant diffeomorphism. In the third part we enumerate the number of conjugacy classes of tori in the diffeomorphism group of torus manifolds. For torus manifolds of dimension greater than six there are always infinitely many conjugacy classes. We give examples which show that this does not hold for six-dimensional torus manifolds. 相似文献
19.
In this article,we investigate the orbit configuration spaces of some equivariant closed manifolds over simple convex polytopes in toric topology,such as small covers,quasi-toric manifolds and(real)moment-angle manifolds;especially for the cases of small covers and quasi-toric manifolds.These kinds of orbit configuration spaces have non-free group actions,and they are all noncompact,but still built via simple convex polytopes.We obtain an explicit formula of the Euler characteristic for orbit configuration spaces of small covers and quasi-toric manifolds in terms of the h-vector of a simple convex polytope.As a by-product of our method,we also obtain a formula of the Euler characteristic for the classical configuration space,which generalizes the Félix-Thomas formula.In addition,we also study the homotopy type of such orbit configuration spaces.In particular,we determine an equivariant strong deformation retraction of the orbit configuration space of 2 distinct orbit-points in a small cover or a quasi-toric manifold,which allows to further study the algebraic topology of such an orbit configuration space by using the Mayer-Vietoris spectral sequence. 相似文献
20.
We announce a comparison formula for two natural definitions of equivariant analytic torsion in de Rham theory. In this formula, a new invariant of equivariant fibrations with odd dimensional compact fibres appears, whose main properties are described. Our results are formally very close to corresponding results which we obtained for holomorphic torsion. 相似文献