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59 paper(s) uploaded by conan.

Index	Title	Upload Time	Modified Time
51	The enumerative geometry of K3 surfaces and modular forms Conan Leung Chinese Univ of HK Jim Bryan Univ British Columbia mathscidoc:1608.01062 Journal of AMS, 13, (2), 371-410, 2000 [ Download ] [ 2016-08-31 17:05:56 uploaded by conan ] [ 772 downloads ] [ 0 comments ] Citation × 1 Katz S, Klemm A, Vafa C, et al. M-Theory, Topological Strings and Spinning Black Holes[J]. Advances in Theoretical and Mathematical Physics, 1999, 3(5): 1445-1537. 2 Ionel E, Parker T H. The Symplectic Sum Formula for Gromov-Witten Invariants[J]. Annals of Mathematics, 2000, 159(3): 935-1025. 3 Marino M, Moore G. Counting higher genus curves in a Calabi-Yau manifold[J]. Nuclear Physics, 1998, 543(3): 592-614. 4 Pandharipande R, Thomas R P. Stable pairs and BPS invariants[J]. Journal of the American Mathematical Society, 2007, 23(1): 267-297. 5 Maulik D, Pandharipande R. A topological view of Gromov-Witten theory[J]. Topology, 2004, 45(5): 887-918. 6 Bryan J, Pandharipande R. BPS states of curves in Calabi--Yau 3--folds[J]. Geometry \u0026 Topology, 2000, 5(1): 287-318. 7 Maulik D, Pandharipande R, Thomas R P, et al. Curves on K3 surfaces and modular forms[J]. Journal of Topology, 2010, 3(4): 937-996. 8 Kazarian M. Multisingularities, cobordisms, and enumerative geometry[J]. Russian Mathematical Surveys, 2003, 58(4): 665-724. 9 Klemm A, Pandharipande R. Enumerative geometry of Calabi-Yau 4-folds[J]. Communications in Mathematical Physics, 2008, 281(3): 621-653. 10 Bayer A, Manin Y I. Semi)simple exercises in quantum cohomology[C]., 2001. More OK [ Cited by 91 ] Abstract × No abstract uploaded! OK [ Abstract ] [ Full ] Please log in for comment!	2016-08-31 17:05:56	-
52	Degeneration of Kahler-Einstein metrics on complete Kahler manifolds Conan Leung Chinese Univ of HK Peng Lu Univ of Minnesota Differential Geometry mathscidoc:1608.10099 Comm Analy Geom, 7, (2), 431-449, 1999 [ Download ] [ 2016-08-31 17:07:14 uploaded by conan ] [ 543 downloads ] [ 0 comments ] Abstract × No abstract uploaded! OK [ Abstract ] [ Full ] Please log in for comment!	2016-08-31 17:07:14	-
53	Generating functions for the number of curves on Abelian surfaces Conan Leung Chinese Univ of HK Jim Bryan Univ British Columbia mathscidoc:1608.01063 Duke Math Journal, 99, (2), 311-328, 1999 [ Download ] [ 2016-08-31 17:08:38 uploaded by conan ] [ 525 downloads ] [ 0 comments ] Citation × 1 Kazarian M. Multisingularities, cobordisms, and enumerative geometry[J]. Russian Mathematical Surveys, 2003, 58(4): 665-724. 2 Steven L Kleiman · Ragni Piene. Node polynomials for families: methods and applications. 2004. 3 Kiem Y, Li J. Localizing virtual cycles by cosections[J]. Journal of the American Mathematical Society, 2010, 26(4): 1025-1050. 4 Kool M, Shende V, Thomas R P, et al. A short proof of the Göttsche conjecture[J]. Geometry \u0026 Topology, 2011, 15(1): 397-406. 5 Martijn Kool · Vivek Shende · R P Thomas. A short proof of the Göttsche conjecture. 2011. 6 Nakajima H. Heisenberg algebra and Hilbert schemes of points on projective surfaces[J]. Annals of Mathematics, 1995, 145(2): 379-388. 7 Kool M, Thomas R P. Reduced classes and curve counting on surfaces I: theory[C]., 2011, 1(3): 334-383. 8 Naichung Conan Leung. Geometric Aspects of Mirror Symmetry (with SYZ for Rigid CY manifolds). 2002. 9 Tianjun Li · Aiko Liu. Family Seiberg-Witten invariants and wall crossing formulas. 2001. 10 Nikolay Qviller. THE DI FRANCESCO–ITZYKSON–GÖTTSCHE CONJECTURES FOR NODE POLYNOMIALS OF ℙ2. 2012. More OK [ Cited by 21 ] Abstract × No abstract uploaded! OK [ Abstract ] [ Full ] Please log in for comment!	2016-08-31 17:08:38	-
54	Counting curves on irrational surfaces Conan Leung Chinese Univ of HK Jim Bryan Univ British Columbia mathscidoc:1608.01064 Surv. Differ. Geom.,, 5, 313-339, 1999 [ Download ] [ 2016-08-31 17:10:13 uploaded by conan ] [ 766 downloads ] [ 0 comments ] Abstract × No abstract uploaded! OK [ Abstract ] [ Full ] Please log in for comment!	2016-08-31 17:10:13	-
55	Symplectic structures on gauge theory Conan Leung Chinese Univ of HK Differential Geometry mathscidoc:1608.10100 Comm Math Phys, 193, 47-67, 1998 [ Download ] [ 2016-08-31 17:11:36 uploaded by conan ] [ 737 downloads ] [ 0 comments ] Abstract × We study certain natural differential forms [] and their G equivariant extensions on the space of connections. These forms are defined using the family local index theorem. When the base manifold is symplectic, they define a family of symplectic forms on the space of connections. We will explain their relationships with the Einstein metric and the stability of vector bundles. These forms also determine primary and secondary characteristic forms (and their higher level generalizations). OK [ Abstract ] [ Full ] Please log in for comment!	2016-08-31 17:11:36	-
56	Bando Futaki invariants and Kahler Einstein metric Conan Leung Chinese Univ of HK Differential Geometry mathscidoc:1608.10101 Comm Analy Geom, 6, (4), 799-808, 1998 [ Download ] [ 2016-08-31 17:12:46 uploaded by conan ] [ 493 downloads ] [ 0 comments ] Abstract × No abstract uploaded! OK [ Abstract ] [ Full ] Please log in for comment!	2016-08-31 17:12:46	-
57	Branes and toric geometry Conan Leung Chinese Univ of HK Cumrum Vafa Harvard University mathscidoc:1608.01065 Adv. Theor. Math. Phys., 2, (1), 91-118, 1998 [ Download ] [ 2016-08-31 17:13:59 uploaded by conan ] [ 675 downloads ] [ 0 comments ] Abstract × No abstract uploaded! OK [ Abstract ] [ Full ] Please log in for comment!	2016-08-31 17:13:59	-
58	Einstein type metrics and stability on vector bundles Conan Leung Chinese Univ of HK Computational Geometry mathscidoc:1608.09015 Journal of Differential Geometry, 45, 514-546, 1997 [ Download ] [ 2016-08-31 17:15:34 uploaded by conan ] [ 753 downloads ] [ 0 comments ] Citation × 1 Marcos Marino · Ruben Minasian · Gregory Moore · Andrew Strominger. Nonlinear Instantons from Supersymmetric p-Branes. 1999. 2 Douglas M R. Dirichlet branes, homological mirror symmetry, and stability[C]., 2002. 3 Blumenhagen R, Moster S, Reinbacher R, et al. Massless spectra of three generation U(N) heterotic string vacua[J]. Journal of High Energy Physics, 2007, 2007(05): 041-041. 4 Aspinwall P S. D-Branes on Calabi-Yau Manifolds[C]., 2004: 1-152. 5 Leung N C, Yau S, Zaslow E, et al. From Special Lagrangian to Hermitian-Yang-Mills via Fourier-Mukai Transform[J]. Advances in Theoretical and Mathematical Physics, 2000, 4(6): 1319-1341. 6 Donagi R, Wijnholt M. Gluing Branes, I[J]. Journal of High Energy Physics, 2011, 2013(5). 7 Xiaowei Wang. Balance point and stability of vector bundles over a projective manifold. 2002. 8 Minasian R, Tomasiello A. Variations on stability[J]. Nuclear Physics, 2001, 631(1): 43-65. 9 Yau S. Perspectives on geometric analysis[C]., 2006, 10(1): 275-379. 10 Hakon Enger · C A Lutken. Non-linear Yang-Mills instantons from strings are $\pi$-stable D-branes. 2003. More OK [ Cited by 18 ] Abstract × In this paper we show that stability for holomorphic vector bundles are equivalent to the existence of solutions to certain system of Monge Ampere equations parametrized by a parameter k. We solve this fully nonlinear elliptic system by singular perturbation technique and show that the vanishing of obstructions for the perturbation is given precisely by the stability condition. This can be interpreted as an infinite dimensional analog of the equivalencybetween Geometric Invariant Theory and Symplectic Reduction for moduli space of vector bundles. OK [ Abstract ] [ Full ] Please log in for comment!	2016-08-31 17:15:34	-
59	Seiberg Witten invariants and uniformizations Conan Leung Chinese Univ of HK Differential Geometry mathscidoc:1608.10102 Math. Ann., 306, 31-46, 1996 [ Download ] [ 2016-08-31 17:16:26 uploaded by conan ] [ 989 downloads ] [ 0 comments ] Citation × 1 Catanese F. Fibred surfaces, varieties isogenous to a product and related moduli spaces[J]. American Journal of Mathematics, 2000, 122(1): 1-44. 2 Vestislav Apostolov · Tedi Drăghici · Andrei Moroianu. A SPLITTING THEOREM FOR KÄHLER MANIFOLDS WHOSE RICCI TENSORS HAVE CONSTANT EIGENVALUES. 2012. 3 Jimmy Petean. Indefinite Kaehler-Einstein metrics on Compact Complex Surfaces. 1996. 4 Hiroyuki Kamada. Self-dual Kähler metrics of neutral signature on complex surfaces. 2002. 5 Lebrun C. The Einstein-Maxwell Equations, Extremal Kahler Metrics, and Seiberg-Witten Theory[C]., 2008: 17-33. 6 Lebrun C. Diffeomorphisms, symplectic forms, and Kodaira fibrations[J]. Geometry \u0026 Topology, 2000, 4(1): 451-456. 7 Lebrun C. Curvature and Smooth Topology in Dimension Four[C]., 2000. 8 Lebrun C. Dieomorphisms, symplectic forms and Kodaira brations[C]., 2000. 9 Leung N C. Uniformization of four manifolds[C]., 1997. 10 Wingsum Cheung · Bun Wong. On a non-abelian invariant on complex surfaces of general type. 2006. More OK [ Cited by 11 ] Abstract × No abstract uploaded! OK [ Abstract ] [ Full ] Please log in for comment!	2016-08-31 17:16:26	-

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