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Mirror partner for a Klein quartic polynomial
Journal of Geometry and Physics. 2025. Vol. 215. Article 105538.
The results of A.~Chiodo, Y.~Ruan and M.~Krawitz associate the mirror partner Calabi--Yau variety $X$ to a Landau--Ginzburg orbifold $(f,G)$ if $f$ is an invertible polynomial satisfying Calabi--Yau condition and the group $G$ is a diagonal symmetry group of $f$.
In this paper we investigate the Landau--Ginzburg orbifolds with a Klein quartic polynomial $f = x_1^3x_2 + x_2^3x_3+x_3^3x_1$ and $G$ being all possible subgroups of $\GL(3,\CC)$, preserving the polynomial~$f$ and also the pairing in its Jacobian algebra. In particular, $G$ is not necessarily abelian or diagonal. The zero--set of polynomial $f$, called Klein quartic, is a genus $3$ smooth compact Riemann surface. We show that its mirror Landau--Ginzburg orbifold is $(f,G)$ with $G$ being a $\ZZ/2\ZZ$--extension of a Klein four--group.
Keywords: mirror symmetry
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We consider 3-diffeomorphisms with source–sink dynamics where Smale solenoids play the role of the source and the sink (NSSS-diffeomorphisms). It is known that such diffeomorphisms exist only on lens spaces. On the 3-sphere, every NSSS-diffeomorphism is associated with an exchangeable braid. An exchangeable braid with the strand number n was constructed for each n 3 in such a way ...
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A classic problem in data analysis is studying the systems of subsets defined by either a similarity or a dissimilarity function on X which is either observed directly or derived from a data set.
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AI errors pose a significant challenge, hindering real-world applications. This work introduces a novel approach to cope with AI errors using weakly supervised error correctors that guarantee a specific level of error reduction. Our correctors have low computational cost and can be used to decide whether to abstain from making an unsafe classification. We provide ...
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Chertopolokhov V., Mukhamedov A., Bugriy G. et al., IEEE Access 2026 Vol. 14 P. 14369–14392
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The approximation of tensors in a low-para metric format is a crucial component in many mathematical modelling and data analysis tasks. Among the widely used low-parametric representations, the canonical polyadic (CP) decomposition is known to be very efficient. Nowadays, most algorithms for CP approximation aim to construct the approximation in the Frobenius norm; however, some ...
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We provide examples of smooth three-dimensional Fano complete intersections of degree 2, 4, 6, and 8 that have absolute coregularity 0. Considering the main theorem of Avilov, Loginov, and Przyjalkowski (CNTP 18:506–577, 2024) on the remaining 101 families of smooth Fano threefolds, our result implies that each family of smooth Fano threefolds has an element of absolute ...
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