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1.
Kenji Fukaya Yong-Geun Oh Hiroshi Ohta Kaoru Ono 《Selecta Mathematica, New Series》2011,17(3):609-711
This is a continuation of part I in the series of the papers on Lagrangian Floer theory on toric manifolds. Using the deformations
of Floer cohomology by the ambient cycles, which we call bulk deformations, we find a continuum of non-displaceable Lagrangian fibers on some compact toric manifolds. We also provide a method of finding
all fibers with non-vanishing Floer cohomology with bulk deformations in arbitrary compact toric manifolds, which we call
bulk-balanced Lagrangian fibers. 相似文献
2.
Hiroshi Iritani 《Mathematische Zeitschrift》2006,252(3):577-622
The objective of this paper is to clarify the relationships between the quantum D-module and equivariant Floer theory. Equivariant Floer theory was introduced by Givental in his paper ``Homological Geometry'.
He conjectured that the quantum D-module of a symplectic manifold is isomorphic to the equivariant Floer cohomology for the universal cover of the free loop
space. First, motivated by the work of Guest, we formulate the notion of ``abstract quantum D-module' which generalizes the D-module defined by the small quantum cohomology algebra. Second, we define the equivariant Floer cohomology of toric complete
intersections rigorously as a D-module, using Givental's model. This is shown to satisfy the axioms of abstract quantum D-module. By Givental's mirror theorem [Giv3], it follows that equivariant Floer cohomology defined here is isomorphic to the
quantum cohomology D-module. 相似文献
3.
In the previous paper [Hiroshi Iritani, Quantum D-modules and equivariant Floer theory for free loop spaces, Math. Z. 252 (3) (2006) 577–622], the author defined equivariant Floer cohomology for a complete intersection in a toric variety and showed that it is isomorphic to the small quantum D-module after a mirror transformation when the first Chern class c1(M) of the tangent bundle is nef. In this paper, even when c1(M) is not nef, we show that the equivariant Floer cohomology reconstructs the big quantum D-module under certain conditions on the ambient toric variety. The proof is based on a mirror theorem of Coates and Givental [T. Coates, A.B. Givental, Quantum Riemann — Roch, Lefschetz and Serre, Ann. of Math. (2) 165 (1) (2007) 15–53]. The reconstruction procedure here gives a generalized mirror transformation first observed by Jinzenji in low degrees [Masao Jinzenji, On the quantum cohomology rings of general type projective hypersurfaces and generalized mirror transformation, Internat. J. Modern Phys. A 15 (11) (2000) 1557–1595; Masao Jinzenji, Co-ordinate change of Gauss–Manin system and generalized mirror transformation, Internat. J. Modern Phys. A 20 (10) (2005) 2131–2156]. 相似文献
4.
We define a quasi–projective reduction of a complex algebraic variety X to be a regular map from X to a quasi–projective variety that is universal with respect to regular maps from X to quasi–projective varieties. A toric quasi–projective reduction is the analogous notion in the category of toric varieties.
For a given toric variety X we first construct a toric quasi–projective reduction. Then we show that X has a quasi–projective reduction if and only if its toric quasi–projective reduction is surjective. We apply this result
to characterize when the action of a subtorus on a quasi–projective toric variety admits a categorical quotient in the category
of quasi–projective varieties.
Received October 29, 1998; in final form December 28, 1998 相似文献
5.
Based on the basis theorem of Bruhat–Chevalley (in Algebraic Groups and Their Generalizations: Classical Methods, Proceedings of Symposia in Pure Mathematics, vol. 56 (part 1), pp. 1–26, AMS, Providence, 1994) and the formula for multiplying Schubert classes obtained in (Duan, Invent. Math. 159:407–436, 2005) and programmed in (Duan and Zhao, Int. J. Algebra Comput. 16:1197–1210, 2006), we introduce a new method for computing the Chow rings of flag varieties (resp. the integral cohomology of homogeneous
spaces). 相似文献
6.
T. E. Panov 《Proceedings of the Steklov Institute of Mathematics》2008,263(1):150-162
In the theory of algebraic group actions on affine varieties, the concept of a Kempf-Ness set is used to replace the categorical
quotient by the quotient with respect to a maximal compact subgroup. Using recent achievements of “toric topology,” we show
that an appropriate notion of a Kempf-Ness set exists for a class of algebraic torus actions on quasiaffine varieties (coordinate
subspace arrangement complements) arising in the Batyrev-Cox “geometric invariant theory” approach to toric varieties. We
proceed by studying the cohomology of these “toric” Kempf-Ness sets. In the case of projective nonsingular toric varieties
the Kempf-Ness sets can be described as complete intersections of real quadrics in a complex space.
Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2008, Vol. 263, pp. 159–172. 相似文献
7.
8.
We calculate the small quantum orbifold cohomology of arbitrary weighted projective spaces. We generalize Givental’s heuristic
argument, which relates small quantum cohomology to S
1-equivariant Floer cohomology of loop space, to weighted projective spaces and use this to conjecture an explicit formula
for the small J-function, a generating function for certain genus-zero Gromov–Witten invariants. We prove this conjecture using a method
due to Bertram. This provides the first non-trivial example of a family of orbifolds of arbitrary dimension for which the
small quantum orbifold cohomology is known. In addition we obtain formulas for the small J-functions of weighted projective complete intersections satisfying a combinatorial condition; this condition naturally singles
out the class of orbifolds with terminal singularities. 相似文献
9.
In this note we study the equivariant cohomology with compact supports of the zeroes of the moment map for the cotangent bundle
of a linear representation of a torus and some of its notable subsets, using the theory of the infinitesimal index, developed
in [8]. We show that, in analogy to the case of equivariant K-theory dealt with in [7] using the index of transversally elliptic operators, we obtain isomorphisms with notable spaces of splines studied in [2], [3]. 相似文献
10.
Jean-Pierre Magnot 《Acta Appl Math》2006,91(1):67-95
We state a Chern–Weil type theorem which is a generalization of a Chern–Weil type theorem for Fredholm structures stated by Freed in [4]. Using this result, we investigate Chern forms on based manifold of maps following two approaches, the first one using the Wodzicki residue, and the second one using renormalized traces of pseudo-differential operators along the lines of [1, 19, 20]. We specialize to the case to study current groups. Finally, we apply these results to a class of holomorphic connections on the loop group . In this last example, we precise Freed's construction [5] on the loop group: The cohomology of the first Chern form of any holomorphic connection in the class considered is given by the Kähler form. 相似文献
11.
Aldo J. Lazar 《Israel Journal of Mathematics》2010,179(1):145-155
We prove that if X is a locally compact σ-compact space, then on its quotient, γ(X) say, determined by the algebra of all real valued bounded continuous functions on X, the quotient topology and the completely regular topology defined by this algebra are equal. It follows from this that if
X is second countable locally compact, then γ(X) is second countable locally compact Hausdorff if and only if it is first countable. The interest in these results originated
in [1] and [7] where the primitive ideal space of a C*-algebra was considered. 相似文献
12.
Brant C. Jones 《Journal of Algebraic Combinatorics》2009,29(2):229-260
We show that the leading coefficient of the Kazhdan–Lusztig polynomial P
x,w
(q) known as μ(x,w) is always either 0 or 1 when w is a Deodhar element of a finite Weyl group. The Deodhar elements have previously been characterized using pattern avoidance
in Billey and Warrington (J. Algebraic Combin. 13(2):111–136, [2001]) and Billey and Jones (Ann. Comb. [2008], to appear). In type A, these elements are precisely the 321-hexagon avoiding permutations. Using Deodhar’s algorithm (Deodhar in Geom. Dedicata
63(1):95–119, [1990]), we provide some combinatorial criteria to determine when μ(x,w)=1 for such permutations w.
The author received support from NSF grants DMS-9983797 and DMS-0636297. 相似文献
13.
We study higher-order conservation laws of the nonlinearizable elliptic Poisson equation as elements of the characteristic
cohomology of the associated exterior differential system. The theory of characteristic cohomology determines a normal form
for differentiated conservation laws by realizing them as elements of the kernel of a linear differential operator. We show
that the
\mathbbS1{\mathbb{S}^1} -symmetry of the PDE leads to a normal form for the undifferentiated conservation laws. Zhiber and Shabat (in Sov Phys Dokl
Akad 24(8):607–609, 1979) determine which potentials of nonlinearizable Poisson equations admit nontrivial Lie–B?cklund transformations. In the case
that such transformations exist, they introduce a pseudo-differential operator that can be used to generate infinitely many
such transformations. We obtain similar results using the theory of characteristic cohomology: we show that for higher-order
conservation laws to exist, it is necessary that the potential satisfies a linear second-order ODE. In this case, at most
two new conservation laws in normal form appear at each even prolongation. By using a recursion motivated by Killing fields,
we show that, for the simplest class of potentials, this upper bound is attained. The recursion circumvents the use of pseudo-differential
operators. We relate higher-order conservation laws to generalized symmetries of the exterior differential system by identifying
their generating functions. This Noether correspondence provides the connection between conservation laws and the canonical
Jacobi fields of Pinkall and Sterling. 相似文献
14.
We consider Lagrangian Floer cohomology for a pair of Lagrangian submanifolds in a symplectic manifold M. Suppose that M carries a symplectic involution, which preserves both submanifolds. Under various topological hypotheses, we prove a localization
theorem for Floer cohomology, which implies a Smith-type inequality for the Floer cohomology groups in M and its fixed point set. Two applications to symplectic Khovanov cohomology are included. 相似文献
15.
Jonas Sunklodas 《Lithuanian Mathematical Journal》2011,51(1):66-74
In this paper, we generalize some results of [V. Bentkus, A new method for approximation in probability and operator theories,
Lith. Math. J., 43(4):367–388, 2003] for independent identically distributed summands to to the case of independent non-identically distributed real summands.
We derive the Edgeworth expansion with the first term only. Proofs are given following [V. Bentkus, A new method for approximation
in probability and operator theories, Lith. Math. J., 43(4):367–388, 2003]. 相似文献
16.
We develop an integral version of Deligne cohomology for smooth proper real varieties. For this purpose the role played by singular cohomology in the complex case has to be replaced by the ordinary bigraded
Gal(\mathbbC/\mathbbR){Gal(\mathbb{C}/{\mathbb{R}})}-equivariant cohomology of Lewis et al. (Bull Am Math Soc (N.S.) 4(2):208–212, 1981), the equivariant counterpart of singular cohomology. The theory is aimed at giving more precise information about the 2-primary
components of regulators. We establish basic properties and give a geometric interpretation for the groups in dimension 2
in weights 1 and 2. 相似文献
17.
We give a bicategorical version of the main result of Masuoka (Tsukuba J Math 13:353–362, 1989) which proposes a non-commutative version of the fact that for a faithfully flat extension of commutative rings R í SR \subseteq S, the relative Picard group Pic(S/R) is isomorphic to the Amitsur 1–cohomology group H
1(S/R,U) with coefficients in the units functor U. 相似文献
18.
Diana Rodelo 《Applied Categorical Structures》2009,17(4):387-418
A new method for realizing the first and second order cohomology groups of an internal abelian group in a Barr-exact category
was introduced by Bourn (Cahiers Topologie Géom Différentielle Catég XL:297–316, 1999; J Pure Appl Algebra 168:133–146, 2002). The main role, in each level, is played by a direction functor. This approach can be generalized to any level n and produces a long exact cohomology sequence. By applying this method to Moore categories we show that they represent a
good context for non-abelian cohomology, in particular for the Baer Extension Theory.
相似文献
19.
In this paper, we continue the investigation of an estimator proposed in [Yu. Davydov, V. Paulauskas, and A. Račkauskas, More
on p-stable convex sets in Banach spaces, J. Theor. Probab., 13:39–64, 2000] and [V. Paulauskas, A new estimator for tail index, Acta Appl. Math., 79:55–67, 2003] and considered in [V. Paulauskas and M. Vaičiulis, Once more on comparison of tail index estimators, preprint, 2010]. We propose a class of modifications of the so-called DPR estimator and demonstrate that these modifications can have better
asymptotic properties than the original DPR estimator. 相似文献
20.
Yizao Wang 《Extremes》2012,15(2):175-196
We provide a necessary and sufficient condition for the ratio of two jointly α-Fréchet random variables to be regularly varying. This condition is based on the spectral representation of the joint distribution
and is easy to check in practice. Our result motivates the notion of the ratio tail index, which quantifies dependence features that are not characterized by the tail dependence index. As an application, we derive the asymptotic behavior of the quotient correlation coefficient proposed in Zhang (Ann Stat
36(2):1007–1030, 2008) in the dependent case. Our result also serves as an example of a new type of regular variation of products, different from
the ones investigated by Maulik et al (J Appl Probab 39(4):671–699, 2002). 相似文献