共查询到20条相似文献,搜索用时 62 毫秒
1.
Xiliang WANG 《Frontiers of Mathematics in China》2021,16(4):1075
Using the degeneration formula, we study the change of Gromov-Witten invariants under blow-up for symplectic 4-manifolds and obtain a genus-decreasing relation of Gromov-Witten invariant of symplectic four manifold under blow-up. 相似文献
2.
Roberto Paoletti 《Israel Journal of Mathematics》2001,123(1):241-251
By working on the symplectic blow-up, we show that the symplectic divisors produced by Donaldson in [D] may be chosen so that
they contain a fixed symplectic submanifold or, in a complementary direction, so that they cut it transversally with a symplectic
intersection. 相似文献
3.
B. Doug Park 《Mathematische Annalen》2002,322(2):267-278
Using Seiberg-Witten theory and rational blow-down procedures of R. Fintushel and R.J. Stern, we construct infinitely many
irreducible smooth structures, both symplectic and non-symplectic, on the four-manifold for each integer n lying in the interval .
Received: 17 January 2000 / Published online: 18 January 2002 相似文献
4.
In this paper, by using the de Rham model of Chen–Ruan cohomology, we define the relative Chen–Ruan cohomology ring for a pair of almost complex orbifold(G, H) with H being an almost sub-orbifold of G. Then we use the Gromov–Witten invariants ofG, the blow-up of G along H,to give a quantum modification of the relative Chen–Ruan cohomology ring H*CR(G, H) when H is a compact symplectic sub-orbifold of the compact symplectic orbifold G. 相似文献
5.
In this paper, one considers the change of orbifold Gromov–Witten invariants under weighted blow-up at smooth points. Some blow-up formula for Gromov–Witten invariants of symplectic orbifolds is proved. These results extend the results of manifolds case to orbifold case. 相似文献
6.
By a result of Kedra and Pinsonnault, we know that the topology of groups of symplectomorphisms of symplectic 4-manifolds is complicated in general. However, in all known (very specific) examples, the rational cohomology rings of symplectomorphism groups are finitely generated. In this paper, we compute the rational homotopy Lie algebra of symplectomorphism groups of the 3-point blow-up of the projective plane (with an arbitrary symplectic form) and show that in some cases, depending on the sizes of the blow-ups, it is infinite dimensional. Moreover, we explain how the topology is generated by the toric structures one can put on the manifold. Our method involve the study of the space of almost complex structures compatible with the symplectic structure and it depends on the inflation technique of Lalonde–McDuff. 相似文献
7.
This paper mainly deals with the type II singularities of the mean curvature flow from a symplectic surface or from an almost calibrated Lagrangian surface in a Kähler surface. The relation between the maximum of the Kähler angle and the maximum of |H|2 on the limit flow is studied. The authors also show the nonexistence of type II blow-up flow of a symplectic mean curvature flow which is normal flat or of an almost calibrated Lagrangian mean curvature flow which is flat. 相似文献
8.
Gil Ramos Cavalcanti 《Transactions of the American Mathematical Society》2007,359(1):333-348
In this paper we study the behaviour of the Lefschetz property under the blow-up construction. We show that it is possible to reduce the dimension of the kernel of the Lefschetz map if we blow up along a suitable submanifold satisfying the Lefschetz property. We use this, together with results about Massey products, to construct compact nonformal symplectic manifolds satisfying the Lefschetz property.
9.
10.
Mihai Halic 《manuscripta mathematica》1999,99(3):371-381
The article investigates the geography of closed, connected and simply connected, six-dimensional manifolds. It is proved
that any triple of integers satisfying some necessary arithmetical restrictions occurs as the Chern triple of such a manifold.
The main tools used for producing the examples are the symplectic connected sum and the symplectic blow-up.
Received: 28 May 1998 / Revised version: 22 January 1999 相似文献
11.
Upper and lower bounds for the Seshadri constants of canonical bundles of compact hyperbolic spaces are given in terms of metric invariants. The lower bound is obtained by carrying out the symplectic blow-up construction for the Poincaré metric, and the upper bound is obtained by a convexity-type argument. 相似文献
12.
Liuqing Yang 《偏微分方程(英文版)》2012,25(3):199-207
In this paper we mainly study the relation between $|A|^2, |H|^2$ and cosα (α is the Kähler angle) of the blow up flow around the type II singularities of a symplectic mean curvature flow. We also study similar property of an almost calibrated Lagrangian mean curvature flow. We show the nonexistence of type II blow-up flows for a symplectic mean curvature flow satisfying $|A|^2≤λ|H|^2$ and $cosα≥δ>1-\frac{1}{2λ}(½≤α≤ 2)$, or for an almost calibrated Lagrangian mean curvature flow satisfying $|A|^2≤λ|H|^2$ and $cosθ≥δ>max\ {0,1-\frac{1}{λ}}(\frac34≤λ≤ 2)$, where θ is the Lagrangian angle. 相似文献
13.
Jaros?aw K?dra 《Differential Geometry and its Applications》2004,21(1):93-112
Moduli spaces of stable pseudoholomorphic curves can be defined parametrically, i.e., over total spaces of symplectic fibrations. This imposes several restrictions on the spectral sequence of a symplectic fibration. We prove, among others, that under certain assumptions the spectral sequence collapses at E2. In the appendix, we prove nontriviality of certain Gromov-Witten invariant for blow-ups. As an application we obtain that any Hamiltonian fibration with the blow-up of along four dimensional submanifold as a fibre c-splits. That is its spectral sequence collapses. 相似文献
14.
In this paper, we study blow-up solutions of the Cauchy problem to the L2 critical nonlinear Schrdinger equation with a Stark potential. Using the variational characterization of the ground state for nonlinear Schrdinger equation without any potential, we obtain some concentration properties of blow-up solutions, including that the origin is the blow-up point of the radial blow-up solutions, the phenomenon of L2-concentration and rate of L2-concentration of blow-up solutions. 相似文献
15.
We introduce a method to resolve a symplectic orbifold(M,ω) into a smooth symplectic manifold . Then we study how the formality and the Lefschetz property of are compared with that of (M,ω). We also study the formality of the symplectic blow-up of (M,ω) along symplectic submanifolds disjoint from the orbifold singularities. This allows us to construct the first example of a simply connected compact symplectic manifold of dimension 8 which satisfies the Lefschetz property but is not formal, therefore giving a counter-example to a conjecture of Babenko and Taimanov. 相似文献
16.
In this article we construct a new simply connected symplectic 4-manifold with b2+=1 and c12=2 which is homeomorphic, but not diffeomorphic, to a rational surface by using rational blow-down technique. As a corollary, we conclude that a rational surface
admits an exotic smooth structure. Mathematics Subject Classification (2000) 53D05, 14J26, 57R55, 57R57 相似文献
17.
In this paper, we investigate the blow-up behavior of solutions of a parabolic equation with localized reactions. We completely classify blow-up solutions into the total blow-up case and the single point blow-up case, and give the blow-up rates of solutions near the blow-up time which improve or extend previous results of several authors. Our proofs rely on the maximum principle, a variant of the eigenfunction method and an initial data construction method. 相似文献
18.
In this article, we investigate the blow-up properties of the positive solutions to a degenerate parabolic system with nonlocal boundary condition. We give the criteria for finite time blow-up or global existence, which shows the important influence of nonlocal boundary. And then we establish the precise blow-up rate estimate for small weighted nonlocal boundary. 相似文献
19.
In this paper we study finite time blow-up of solutions
of a hyperbolic model for chemotaxis. Using appropriate scaling
this hyperbolic model leads to a parabolic model as studied by
Othmer and Stevens (1997) and Levine and Sleeman (1997). In the
latter paper, explicit solutions which blow-up in finite time were
constructed. Here, we adapt their method to construct a
corresponding blow-up solution of the hyperbolic model. This
construction enables us to compare the blow-up times of the
corresponding models. We find that the hyperbolic blow-up is
always later than the parabolic blow-up. Moreover, we show that
solutions of the hyperbolic problem become negative near blow-up.
We calculate the zero-turning-rate time explicitly and we show
that this time can be either larger or smaller than the parabolic
blow-up time.
The blow-up models as discussed here and elsewhere are limiting
cases of more realistic models for chemotaxis. At the end of the
paper we discuss the relevance to biology and exhibit numerical
solutions of more realistic models. 相似文献
20.
Mahuya Datta 《Proceedings Mathematical Sciences》1998,108(2):137-149
In this paper we give a homotopy classification of symplectic isometric immersions following Gromov’sh-principle theorem. 相似文献