Orbifold quantum D-modules associated to weighted projective spaces
نویسندگان
چکیده
منابع مشابه
Orbifold Quantum Cohomology of Weighted Projective Spaces
In this article, we prove the following results. • We show a mirror theorem : the Frobenius manifold associated to the orbifold quantum cohomology of weighted projective space is isomorphic to the one attached to a specific Laurent polynomial, • We show a reconstruction theorem, that is, we can reconstruct in an algorithmic way the full genus 0 Gromov-Witten potential from the 3-point invariants.
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Chen and Ruan [6] defined a very interesting cohomology theoryChen-Ruan orbifold cohomology. The primary objective of this paper is to compute the Chen-Ruan orbifold cohomology of the weighted projective spaces, one of the most important space used in physics. The classical tools (orbifold cohomology defined by Chen and Ruan, toric varieties, the localization technique) which have been proved t...
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We calculate the small quantum orbifold cohomology of arbitrary weighted projective spaces. We generalize Givental’s heuristic argument, which relates small quantum cohomology to S-equivariant Floer cohomology of loop space, to weighted projective spaces and use this to conjecture an explicit formula for the small J-function, a generating function for certain genuszero Gromov–Witten invariants....
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We construct explicit generators of the K-theory and K-homology for the coordinate algebra of ‘functions’ on the quantum projective spaces. We also sketch a construction of unbounded Fredholm modules, that is to say Dirac-like operators and spectral triples of any positive real dimension.
متن کاملCrepant Resolutions of Weighted Projective Spaces and Quantum Deformations
We compare the Chen-Ruan cohomology ring of the weighted projective spaces P(1, 3, 4, 4) and P(1, ..., 1, n) with the cohomology ring of their crepant resolutions. In both cases, we prove that the Chen-Ruan cohomology ring is isomorphic to the quantum corrected cohomology ring of the crepant resolution after suitable evaluation of the quantum parameters. For this, we prove a formula for the Gro...
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ژورنال
عنوان ژورنال: Commentarii Mathematici Helvetici
سال: 2014
ISSN: 0010-2571
DOI: 10.4171/cmh/319