首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 0 毫秒
1.
We define tropical Psi-classes on\({\mathcal{M}_{0,n}(\mathbb{R}^2, d)}\) and consider intersection products of Psi-classes and pull-backs of evaluations on this space. We show a certain WDVV equation which is sufficient to prove that tropical numbers of curves satisfying certain Psi- and evaluation conditions are equal to the corresponding classical numbers. We present an algorithm that generalizes Mikhalkin’s lattice path algorithm and counts rational plane tropical curves satisfying certain Psi- and evaluation conditions.  相似文献   

2.
Let $L$ be a closed orientable Lagrangian submanifold of a closed symplectic six-manifold $(X , \omega )$ . We assume that the first homology group $H_1 (L ; A)$ with coefficients in a commutative ring $A$ injects into the group $H_1 (X ; A)$ and that $X$ contains no Maslov zero pseudo-holomorphic disc with boundary on $L$ . Then, we prove that for every generic choice of a tame almost-complex structure $J$ on $X$ , every relative homology class $d \in H_2 (X , L ; \mathbb{Z })$ and adequate number of incidence conditions in $L$ or $X$ , the weighted number of $J$ -holomorphic discs with boundary on $L$ , homologous to $d$ , and either irreducible or reducible disconnected, which satisfy the conditions, does not depend on the generic choice of $J$ , provided that at least one incidence condition lies in $L$ . These numbers thus define open Gromov–Witten invariants in dimension six, taking values in the ring $A$ .  相似文献   

3.
We compute local Gromov–Witten invariants of cubic surfaces at all genera. We use a deformation a of cubic surface to a nef toric surface and the deformation invariance of Gromov–Witten invariants.  相似文献   

4.
We relate the genus zero gauged Gromov–Witten invariants of a smooth projective variety for sufficiently small area with equivariant Gromov–Witten invariants. As an application we deduce a gauged version of abelianization for Gromov–Witten invariants in the small area chamber. In the symplectic setting, we prove that any sequence of genus zero symplectic vortices with vanishing area has a subsequence that converges after gauge transformation to a holomorphic map with zero average moment map.  相似文献   

5.
6.
We establish a formula for the Gromov–Witten–Welschinger invariants of \(\mathbb {C}P^3\) with mixed real and conjugate point constraints. The method is based on a suggestion by J. Kollár that, considering pencils of quadrics, some real and complex enumerative invariants of \(\mathbb {C}P^3\) could be computed in terms of enumerative invariants of \(\mathbb {C}P^1\times \mathbb {C}P^1\) and of elliptic curves.  相似文献   

7.
Recently, L. Rozansky and E. Witten associated to any hyper-Kähler manifold X a system of weights (numbers, one for each trivalent graph) and used them to construct invariants of topological 3-manifolds. We give a simple cohomological definition of these weights in terms of the Atiyah class of X (the obstruction to the existence of a holomorphic connection). We show that the analogy between the tensor of curvature of a hyper-Kähler metric and the tensor of structure constants of a Lie algebra observed by Rozansky and Witten, holds in fact for any complex manifold, if we work at the level of cohomology and for any Kähler manifold, if we work at the level of Dolbeault cochains. As an outcome of our considerations, we give a formula for Rozansky–Witten classes using any Kähler metric on a holomorphic symplectic manifold.  相似文献   

8.
In this paper, using the gluing formula of Gromov–Witten invariants for symplectic cutting developed by Li and Ruan, we established some relations between Gromov–Witten invariants of a semipositive symplectic manifold M and its blow-ups along a smooth surface.  相似文献   

9.
We represent stationary descendant Gromov–Witten invariants of projective space, up to explicit combinatorial factors, by polynomials. One application gives the asymptotic behaviour of the large degree behaviour of stationary descendant Gromov–Witten invariants in terms of intersection numbers over the moduli space of curves. We also show that primary Gromov–Witten invariants are"virtual" stationary descendants and hence the string and divisor equations can be understood purely in terms of stationary invariants.  相似文献   

10.
《Advances in Mathematics》2013,232(1):238-270
Let (X,ω) be a symplectic manifold and L be a Lagrangian submanifold diffeomorphic to Sn, RPn, or a Lens space of a certain type. Using the symplectic cut and symplectic sum constructions, we express the open Gromov–Witten invariants of (X,L) in terms of open Gromov–Witten invariants of a pair (X,L) determined by L and the standard Gromov–Witten invariants of a symplectic manifold X+ determined by (X,L). We also describe other applications of this approach.  相似文献   

11.
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   

12.
In this paper, we study genus 0 equivariant relative Gromov–Witten invariants of P1 whose corresponding relative stable maps are totally ramified over one point. For fixed number of marked points, we show that such invariants are piecewise polynomials in some parameter space. The parameter space can then be divided into polynomial domains, called chambers. We determine the difference of polynomials between two neighbouring chambers. In some special chamber, which we called the totally negative chamber, we show that such a polynomial can be expressed in a simple way. The chamber structure here shares some similarities to that of double Hurwitz numbers.  相似文献   

13.
We consider a modified version of the Seiberg–Witten invariants for rational homology 3-spheres, obtained by adding to the original invariants a correction term which is a combination of -invariants. We show that these modified invariants are topological invariants. We prove that an averaged version of these modified invariants equals the Casson–Walker invariant. In particular, this result proves an averaged version of a conjecture of Ozsváth and Szabó on the equivalence between their invariant and the Seiberg–Witten invariant of rational homology 3-spheres.  相似文献   

14.
15.
We examine potential extensions of the Stiefel–Whitney invariants from quadratic forms to bilinear forms which are not necessarily symmetric. We show that as long as the symbolic nature of the invariants is maintained, some natural extensions carry only low dimensional information. In particular, the generic invariant on upper triangular matrices is equivalent to the dimension and determinant. Along the process, we show that every non-alternating matrix is congruent to an upper triangular matrix, and prove a version of Witt?s Chain Lemma for upper-triangular bases. (The classical lemma holds for orthogonal bases.)  相似文献   

16.
17.
18.
We extend the Gallot–Tanno theorem to closed pseudo-Riemannian manifolds. It is done by showing that if the cone over a manifold admits a parallel symmetric (0, 2)-tensor then it is Riemannian. Applications of this result to the existence of metrics with distinct Levi-Civita connections but having the same unparametrized geodesics and to the projective Obata conjecture are given. We also apply our result to show that the holonomy group of a closed (O(p + 1, q), S p,q )-manifold does not preserve any nondegenerate splitting of \mathbb Rp+1,q{\mathbb {R}^{p+1,q}}.  相似文献   

19.
In this paper, the differential invariants of Lie symmetry groups of Hirota–Ramani (HR) equation and Drinfel’d–Sokolov–Wilson (DSW) system are obtained and their syzygies and recurrence relations are classified. The algorithms are based on the method of equivariant moving frames.  相似文献   

20.
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号