Homological mirror symmetry and tropical geometry
著者
書誌事項
Homological mirror symmetry and tropical geometry
(Lecture notes of the Unione matematica italiana, 15)
Springer : UMI, c2014
大学図書館所蔵 全16件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Other editors: Fabrizio Catanese, Maxim Kontsevich, Tony Pantev, Yan Soibelman, Ilia Zharkov
Includes bibliographical references
内容説明・目次
内容説明
The relationship between Tropical Geometry and Mirror Symmetry goes back to the work of Kontsevich and Y. Soibelman (2000), who applied methods of non-archimedean geometry (in particular, tropical curves) to Homological Mirror Symmetry. In combination with the subsequent work of Mikhalkin on the "tropical" approach to Gromov-Witten theory and the work of Gross and Siebert, Tropical Geometry has now become a powerful tool. Homological Mirror Symmetry is the area of mathematics concentrated around several categorical equivalences connecting symplectic and holomorphic (or algebraic) geometry. The central ideas first appeared in the work of Maxim Kontsevich (1993). Roughly speaking, the subject can be approached in two ways: either one uses Lagrangian torus fibrations of Calabi-Yau manifolds (the so-called Strominger-Yau-Zaslow picture, further developed by Kontsevich and Soibelman) or one uses Lefschetz fibrations of symplectic manifolds (suggested by Kontsevich and further developed by Seidel). Tropical Geometry studies piecewise-linear objects which appear as "degenerations" of the corresponding algebro-geometric objects.
目次
Oren Ben-Bassat and Elizabeth Gasparim: Moduli Stacks of Bundles on Local Surfaces.- David Favero, Fabian Haiden and Ludmil Katzarkov: An orbit construction of phantoms, Orlov spectra and Knoerrer Periodicity.- Stephane Guillermou and Pierre Schapira: Microlocal theory of sheaves and Tamarkin's non displaceability theorem.- Sergei Gukov and Piotr Sulkowski: A-polynomial, B-model and Quantization.- M. Kapranov, O. Schiffmann, E. Vasserot: Spherical Hall Algebra of Spec(Z).- Maxim Kontsevich and Yan Soibelman: Wall-crossing structures in Donaldson-Thomas invariants, integrable systems and mirror Symmetry.- Grigory Mikhalkin and Ilia Zharkov: Tropical eigen wave and intermediate Jacobians.- Andrew Neitzke: Notes on a new construction of hyperkahler metrics.- Helge Ruddat: Mirror duality of Landau-Ginzburg models via Discrete Legendre Transforms.- Nicolo Sibilla: Mirror Symmetry in dimension one and Fourier-Mukai transforms.- Alexander Soibelman: The very good property for moduli of parabolic bundles and the additive Deligne-Simpson problem.
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