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Search Results: 1 - 10 of 27703 matches for " Jianxun Hu "
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Local Gromov-Witten invariants of Blowups of Fano surfaces
Jianxun Hu
Mathematics , 2010, DOI: 10.1016/j.geomphys.2011.02.004
Abstract: In this paper, using the degeneration formula we obtain a blowup formulae of local Gromov-Witten invariants of Fano surfaces. This formula makes it possible to compute the local Gromov-Witten invariants of non-toric Fano surfaces form toric Fano surface, such as del Pezzo surfaces. This formula also verifed an expectation of Chiang-Klemm-Yau-Zaslow.
Local Donaldson-Thomas invariants of Blowups of surfaces
Jianxun Hu
Mathematics , 2011,
Abstract: Using the degeneration formula for Donaldson-Thomas invariants, we proved a formula for the change of Donaldson-Thomas invariants of local surfaces under blowing up along points.
Gromov-Witten Invariants of Blow-ups Along Points and Curces
Jianxun Hu
Mathematics , 1998,
Abstract: In this paper, using the gluing formula of Gromov-Witten invariants under symplectic cutting, due to Li and Ruan, we studied the Gromov-Witten invariants of blow-ups at a smooth point or along a smooth curve. We established some relations between Gromov-Witten invariants of M and its blow-ups at a smooth point or along a smooth curve.
Positive divisors in symplectic geometry
Jianxun Hu,Yongbin Ruan
Mathematics , 2008,
Abstract: In this paper, we gave some explicit relations between absolute and relative Gromov-Witten invariants. We proved that a symplectic manifold is symplectic rationally connected if it contains a positive divisor symplectomorphic to $P^n$.
Mukai Flop and Ruan Cohomology
Jianxun Hu,Wanchuan Zhang
Mathematics , 2003,
Abstract: Suppose that two compact manifolds $X, X'$ are connected by a sequence of Mukai flops. In this paper, we construct a ring isomorphism between cohomology ring of $X$ and $X'$. Using the local mirror symmetry technique, we prove that the quantum corrected products on $X, X'$ are the ordinary intersection products. Furthermore, $X, X'$ have isomorphic Ruan cohomology. i.e. we proved the cohomological minimal model conjecture proposed by Ruan.
Orbifold Gromov-Witten Invariants of Weighted Blow-up at Smooth Points
Weiqiang He,Jianxun Hu
Mathematics , 2013,
Abstract: 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.
The Weinstein Conjecture in Product of Symplectic Manifolds
Yanqiao Ding,Jianxun Hu
Mathematics , 2015,
Abstract: In this paper, using pseudo-holomorphic curve method, one proves the Weinstein conjecture in the product $P_1\times P_2$ of two strongly geometrically bounded symplectic manifolds under some conditions with $P_1$. In particular, if $N$ is a closed manifold or a noncompact manifold of finite topological type, our result implies that the Weinstein conjecture in $\mathbb{C}\mathbb{P}^2\times T^*N$ holds.
Elliptic GW invariants of blowups along curves and surfaces
Jianxun Hu,Hou-Yang Zhang
International Journal of Mathematics and Mathematical Sciences , 2005, DOI: 10.1155/ijmms.2005.81
Abstract: We established a relation between elliptic Gromov-Witten invariants of a symplectic manifold M and its blowups along smooth curves and surfaces.
Delocalized Chern character for stringy orbifold K-theory
Jianxun Hu,Bai-Ling Wang
Mathematics , 2011,
Abstract: In this paper, we define a stringy product on $K^*_{orb}(\XX) \otimes \C $, the orbifold K-theory of any almost complex presentable orbifold $\XX$. We establish that under this stringy product, the de-locaized Chern character ch_{deloc} : K^*_{orb}(\XX) \otimes \C \longrightarrow H^*_{CR}(\XX), after a canonical modification, is a ring isomorphism. Here $ H^*_{CR}(\XX)$ is the Chen-Ruan cohomology of $\XX$. The proof relies on an intrinsic description of the obstruction bundles in the construction of Chen-Ruan product. As an application, we investigate this stringy product on the equivariant K-theory $K^*_G(G)$ of a finite group $G$ with the conjugation action. It turns out that the stringy product is different from the Pontryajin product (the latter is also called the fusion product in string theory).
The Donaldson-Thomas invariants under blowups and flops
Jianxun Hu,Wei-Ping Li
Mathematics , 2005,
Abstract: Using the degeneration formula for Doanldson-Thomas invariants, we proved formulae for blowing up a point and simple flops.
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