Quantum cohomology via D-modules

研究成果: Article

18 引用 (Scopus)

抄録

We propose a new point of view on quantum cohomology, motivated by the work of Givental and Dubrovin, but closer to differential geometry than the existing approaches. The central object is a D-module which "quantizes" a commutative algebra associated to the (uncompactified) space of rational curves. Under appropriate conditions, we show that the associated flat connection may be gauged to the flat connection underlying quantum cohomology. This method clarifies the role of the Birkhoff factorization in the "mirror transformation", and it gives a new algorithm (requiring construction of a Groebner basis and solution of a system of o.d.e.) for computation of the quantum product.

元の言語English
ページ(範囲)263-281
ページ数19
ジャーナルTopology
44
発行部数2
DOI
出版物ステータスPublished - 2005 3
外部発表Yes

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Quantum Cohomology
Flat Connection
D-module
Groebner Basis
Rational Curves
Commutative Algebra
Differential Geometry
Factorization
Mirror
Object

ASJC Scopus subject areas

  • Geometry and Topology

これを引用

Quantum cohomology via D-modules. / Guest, Martin.

:: Topology, 巻 44, 番号 2, 03.2005, p. 263-281.

研究成果: Article

Guest, Martin. / Quantum cohomology via D-modules. :: Topology. 2005 ; 巻 44, 番号 2. pp. 263-281.
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