Mathematics – Algebraic Geometry
Scientific paper
2011-12-07
Mathematics
Algebraic Geometry
60 pages, 1 figure
Scientific paper
On a smooth projective variety with k ample line bundles, we denote by Z the complete intersection subvariety defined by generic sections. We define the twisted quantum D-module which is a vector bundle with a flat connection, a flat pairing and a natural integrable structure. An appropriate quotient of it is isomorphic to the ambient part of the quantum D-module of Z. When the variety is toric, these quantum D-modules are cyclic. The twisted quantum D-module can be presented via mirror symmetry by the GKZ system associated to the total space of the dual of the direct sum of these line bundles. A question is to know what is the system of equations that define the ambiant part of the quantum D-module of Z. We construct this system as a quotient ideal of the GKZ system. We also state and prove the non-equivariant twisted Gromov-Witten axioms in the appendix.
Mann Etienne
Mignon Thierry
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