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Relevant bibliographies by topics / Kontsevich–Soibelman structure

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Academic literature on the topic 'Kontsevich–Soibelman structure'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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Journal articles on the topic "Kontsevich–Soibelman structure"

1

Nicaise, Johannes, Chenyang Xu, and Tony Yue Yu. "The non-archimedean SYZ fibration." Compositio Mathematica 155, no. 5 (2019): 953–72. http://dx.doi.org/10.1112/s0010437x19007152.

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We construct non-archimedean SYZ (Strominger–Yau–Zaslow) fibrations for maximally degenerate Calabi–Yau varieties, and we show that they are affinoid torus fibrations away from a codimension-two subset of the base. This confirms a prediction by Kontsevich and Soibelman. We also give an explicit description of the induced integral affine structure on the base of the SYZ fibration. Our main technical tool is a study of the structure of minimal dlt (divisorially log terminal) models along one-dimensional strata.

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2

Davison, Ben, Davesh Maulik, Jörg Schürmann, and Balázs Szendrői. "Purity for graded potentials and quantum cluster positivity." Compositio Mathematica 151, no. 10 (2015): 1913–44. http://dx.doi.org/10.1112/s0010437x15007332.

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Consider a smooth quasi-projective variety $X$ equipped with a $\mathbb{C}^{\ast }$-action, and a regular function $f:X\rightarrow \mathbb{C}$ which is $\mathbb{C}^{\ast }$-equivariant with respect to a positive weight action on the base. We prove the purity of the mixed Hodge structure and the hard Lefschetz theorem on the cohomology of the vanishing cycle complex of $f$ on proper components of the critical locus of $f$, generalizing a result of Steenbrink for isolated quasi-homogeneous singularities. Building on work by Kontsevich and Soibelman, Nagao, and Efimov, we use this result to prove

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3

Efimov, Alexander I. "Cohomological Hall algebra of a symmetric quiver." Compositio Mathematica 148, no. 4 (2012): 1133–46. http://dx.doi.org/10.1112/s0010437x12000152.

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AbstractIn [M. Kontsevich and Y. Soibelman, Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson–Thomas invariants, Preprint (2011), arXiv:1006.2706v2[math.AG]], the authors, in particular, associate to each finite quiver Q with a set of vertices I the so-called cohomological Hall algebra ℋ, which is ℤI≥0-graded. Its graded component ℋγ is defined as cohomology of the Artin moduli stack of representations with dimension vector γ. The product comes from natural correspondences which parameterize extensions of representations. In the case of a symmetric quiver, one can

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4

Chaimanowong, W., P. Norbury, M. Swaddle, and M. Tavakol. "Airy structures and deformations of curves in surfaces." Journal of the London Mathematical Society, November 27, 2023. http://dx.doi.org/10.1112/jlms.12839.

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AbstractAn embedded curve in a symplectic surface defines a smooth deformation space of nearby embedded curves. A key idea of Kontsevich and Soibelman is to equip the symplectic surface with a foliation in order to study the deformation space . The foliation, together with a vector space of meromorphic differentials on , endows an embedded curve with the structure of the initial data of topological recursion, which defines a collection of symmetric tensors on . Kontsevich and Soibelman define an Airy structure on to be a formal quadratic Lagrangian which leads to an alternative construction of

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5

Borot, Gaëtan, Vincent Bouchard, Nitin Chidambaram, Thomas Creutzig та Dmitry Noshchenko. "Higher Airy Structures, 𝒲 Algebras and Topological Recursion". Memoirs of the American Mathematical Society 296, № 1476 (2024). http://dx.doi.org/10.1090/memo/1476.

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We define higher quantum Airy structures as generalizations of the Kontsevich–Soibelman quantum Airy structures by allowing differential operators of arbitrary order (instead of only quadratic). We construct many classes of examples of higher quantum Airy structures as modules of W ( g ) \mathcal {W}(\mathfrak {g}) algebras at self-dual level, with g = g l N + 1 \mathfrak {g}= \mathfrak {gl}_{N+1} , s o 2 N \mathfrak {so}_{2 N } or e N \mathfrak {e}_N . We discuss their enumerative geometric meaning in the context of (open and closed) intersection theory of the moduli space of curves and its v

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6

Emmerson, Parker Yaohushuason. "Geometry of Phenomenological Velocity: Energy Numbers, Curvature and Fukaya-Type Categories." May 27, 2025. https://doi.org/10.5281/zenodo.15523017.

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Thank you, Yaohushua for letting me continue to distribute these mathematical gesturing forms so interesting. The paper constructs an algebraic–geometric framework around the “phenomenological ve-locity” expression v = pN/D that arose in previous informal work. We introduce (i) theenergy-number field E, (ii) a non-commutative velocity-string algebra V, (iii) a curvature scalarKPV defined from a “PV–Hessian”, and (iv) a curved A∞ category Fukv (M ) obtained from anordinary Fukaya category by multiplication with v. Basic structural results are proved; se

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