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  On quantum cohomology of Grassmannians of isotropic lines, unfoldings An-singularities, and Lefschetz exceptional collections

Cruz Morales, J. A., Kuznetsov, A., Mellit, A., Perrin, N., & Smirnov, M. (2019). On quantum cohomology of Grassmannians of isotropic lines, unfoldings An-singularities, and Lefschetz exceptional collections. Annales de l'Institut Fourier, 69(3), 955-991. Retrieved from http://arxiv.org/abs/1705.01819.

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Latex : On quantum cohomology of Grassmannians of isotropic lines, unfoldings of $A_n$-singularities, and Lefschetz exceptional collections

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Cruz Morales-Mellit-Perrin-Smirnov_On quantum cohomology of Grassmannians of isotropic lines_2019.pdf (Publisher version), 4MB
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Cruz Morales-Mellit-Perrin-Smirnov_On quantum cohomology of Grassmannians of isotropic lines_2019.pdf
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Cet article est mis à disposition selon les termes de la licence Creative Commons attribution – pas de modification 3.0 France

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Cruz Morales, John Alexander1, Author           
Kuznetsov, Alexander, Author
Mellit, Anton, Author
Perrin, Nicolas, Author
Smirnov, Maxim1, Author           
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Algebraic Geometry,Rings and Algebras, Symplectic Geometry
 Abstract: The subject of this paper is the big quantum cohomology rings of symplectic isotropic Grassmannians $\text{IG}(2, 2n)$. We show that these rings are regular. In particular, by "generic smoothness", we obtain a conceptual proof of generic semisimplicity of the big quantum cohomology for $\text{IG}(2, 2n)$.
Further, by a general result of Claus Hertling, the regularity of these rings implies that they have a description in terms of isolated hypersurface singularities, which we show in this case to be of type $A_{n-1}$. By the homological mirror symmetry conjecture, these results suggest the existence of a very special full exceptional collection in the derived category of coherent sheaves on $\text{IG}(2, 2n)$. Such a collection is constructed in the appendix by Alexander Kuznetsov.

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Language(s): eng - English
 Dates: 2019
 Publication Status: Issued
 Pages: 37
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 1705.01819
URI: http://arxiv.org/abs/1705.01819
 Degree: -

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Title: Annales de l'Institut Fourier
Source Genre: Journal
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Publ. Info: Institut Fourier
Pages: - Volume / Issue: 69 (3) Sequence Number: - Start / End Page: 955 - 991 Identifier: ISSN: 0373-0956