2008年9月
Quantum D-modules and generalized mirror transformations
TOPOLOGY
- 巻
- 47
- 号
- 4
- 開始ページ
- 225
- 終了ページ
- 276
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1016/j.top.2007.07.001
- 出版者・発行元
- PERGAMON-ELSEVIER SCIENCE LTD
In the previous paper [Hiroshi Iritani, Quantum D-modules and equivariant Floer theory for free loop spaces, Math. Z. 252 (3) (2006) 577-622], the author defined equivariant Floer cohomology for a complete intersection in a toric variety and showed that it is isomorphic to the small quantum D-module after a mirror transformation when the first Chern class c(1)(M) of the tangent bundle is nef. In this paper, even when c1(M) is not nef, we show that the equivariant Floer cohomology reconstructs the big quantum D-module under certain conditions on the ambient toric variety. The proof is based on a mirror theorem of Coates and Givental [T. Coates, A. B. Givental, Quantum Riemann - Roch, Lefschetz and Serre, Ann. of Math. (2) 165 (1) (2007) 15 - 53]. The reconstruction procedure here gives a generalized mirror transformation first observed by Jinzenji in low degrees [Masao Jinzenji, On the quantum cohomology rings of general type projective hypersurfaces and generalized mirror transformation, Internat. J. Modern Phys. A 15 (11) (2000) 1557 - 1595; Masao Jinzenji, Co-ordinate change of Gauss-Manin system and generalized mirror transformation, Internat. J. Modern Phys. A 20 (10) (2005) 2131 - 2156]. (C) 2007 Elsevier Ltd. All rights reserved.
- リンク情報
- ID情報
-
- DOI : 10.1016/j.top.2007.07.001
- ISSN : 0040-9383
- Web of Science ID : WOS:000273020400002