記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：JAPAN ACAD  

We construct an integrable system on an open subset of a Fano manifold equipped with a toric degeneration, and compute the potential function for its Lagrangian torus fiber if the central fiber is a tone Fano variety admitting a small resolution.

DOI： 10.3792/pjaa.88.31

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：ACADEMIC PRESS INC ELSEVIER SCIENCE  

We define a tonic degeneration of an integrable system on a projective manifold, and prove the existence of a tonic degeneration of the Gelfand-Cetlin system on the flag manifold of type A, As an application, we calculate the potential function for a Lagrangian torus fiber of the Gelfand-Cetlin system. (C) 2009 Elsevier Inc. All rights reserved.

DOI： 10.1016/j.aim.2009.12.012

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：AMER INST PHYSICS  

We prove a convergence theorem for a sequence of anti-self-dual connections on a family of products of two Riemann surfaces, where the metric of one factor shrinks, establishing the conjecture of Bershadsky et al. [Topological reduction of 4D SYM to 2D sigma-models," Nucl. Phys. B 448, 166 (1995)]. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3318164]

DOI： 10.1063/1.3318164

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：WORLD SCIENTIFIC PUBL CO PTE LTD  

In this paper, we will construct a global gauge for connections with small curvature on the trivial complex rank 2 bundle on T-2. In this gauge the connection matrix A satisfies parallel to A parallel to (Cr+1) <= const. parallel to FA parallel to(1/2)(Cr).

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：DUKE UNIV PRESS  

We show that the counting of rational curves on a complete toric variety which are in general position relative to the toric prime divisors coincides with the counting of certain tropical curves. The proof is algebraic-geometric and relies on degeneration techniques and log deformation theory.

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：KINOKUNIYA CO LTD  

We construct a family of examples of non-zero relative homolgy classes on some infinite dimensional spaces of symplectic forms.

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