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Frobenius map for quintic threefolds
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The matrix of the Frobenius map on the middle dimensional cohomology of the one parameter family that is related by mirror symmetry to the family of all quintic threefolds was calculated in this paper.Abstract:
We calculate the matrix of the Frobenius map on the middle dimensional cohomology of the one parameter family that is related by mirror symmetry to the family of all quintic threefolds.read more
Citations
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Journal ArticleDOI
Twisted de Rham cohomology, homological definition of the integral and “Physics over a ring”
Albert Schwarz,Ilya L. Shapiro +1 more
TL;DR: In this paper, the twisted de Rham cohomology was used to define the Frobenius map on the p-adic cohomeology and to define a family of integrals for topological quantum field theories.
Journal ArticleDOI
Integrality theorems in the theory of topological strings
Albert Schwarz,Vadim Vologodsky +1 more
TL;DR: In this article, a simplified derivation of instanton numbers and of mirror map in terms of Frobenius map on p -adic cohomology was given, and this expression was used to prove integrality theorems.
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Frobenius structures on hypergeometric equations
N Lotca,Kiran S. Kedlaya +1 more
TL;DR: In this article, Dwork's construction of Frobenius structures associated to generalized hypergeometric equations via the interpretation of the latter due to Gelfand-Kapranov-Zelevinsky in the language of A-hypergeometric systems is given.
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Frobenius map and the $p$-adic Gamma function
TL;DR: In this paper, the authors studied the relationship between the power series expansion of the Dwork exponential and the Mahler expansion of Gamma function and showed that certain quantities that appeared in previous computations of the Frobenius map can be expressed in terms of the derivatives of the $p$-adic Gamma function at 0.
Book ChapterDOI
Introduction to Arithmetic Mirror Symmetry
TL;DR: In this paper, it was shown that the number of points of a generic element can be given in terms of p-adic period integrals and Picard-Fuchs differential equations for certain one-parameter families of Calabi-Yau manifolds.
References
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Book
Mirror symmetry and algebraic geometry
David A. Cox,Sheldon Katz +1 more
TL;DR: The quintic threefold Toric geometry Mirror symmetry constructions Hodge theory and Yukawa couplings Moduli spaces Gromov-Witten invariants Quantum cohomology Localization Quantum differential equations The mirror theorem Conclusion Singular varieties Physical theories Bibliography Index as mentioned in this paper
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p-adic multiple zeta values I. p-adic multiple polylogarithms and the p-adic KZ equation
TL;DR: The main aim in this paper is to give a foundation of the theory of p-adic multiple zeta values, which are sometimes analogous to the complex case and are sometimes peculiar to thep-adic case, via the P-adic KZ equation.
Journal ArticleDOI
On the differential equations satisfied by period matrices
TL;DR: In this paper, the authors implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/legal.php).
Journal ArticleDOI
Integrality of instanton numbers and p-adic B-model
TL;DR: In this article, the integrality of instanton numbers (genus zero Gopakumar-Vafa invariants) for quintic and other Calabi-Yau manifolds was studied.