On the geometry of the Hermitian Veronese curve and its quasi-Hermitian surfaces [PDF]
Discrete Mathematics, 2023 The complete classification of the orbits on subspaces under the action of the projective stabiliser of (classical) algebraic varieties is a challenging task, and few classifications are complete.
Stefano Lia +2 more
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Generalized Weierstrass semigroups at several points on certain maximal curves which cannot be covered by the Hermitian curve [PDF]
Designs, Codes and Cryptography, 2021 In this paper we determine the generalized Weierstrass semigroup $$ \widehat{H}(P_{\infty }, P_1, \ldots , P_{m})$$ H ^ ( P ∞ , P 1 , … , P m ) , and consequently the Weierstrass semigroup $$H(P_{\infty }, P_1, \ldots , P_{m})$$ H ( P ∞ , P 1 , … , P m )
M. Montanucci, G. Tizziotti
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Compact connected components in relative character varieties of punctured spheres [PDF]
Épijournal de Géométrie Algébrique, 2021 We prove that some relative character varieties of the fundamental group of a punctured sphere into the Hermitian Lie groups $\mathrm{SU}(p,q)$ admit compact connected components.
Nicolas Tholozan, Jérémy Toulisse
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An Algorithmic Approach to Entanglement-Assisted Quantum Error-Correcting Codes from the Hermitian Curve [PDF]
Advances in Mathematics of Communications, 2021 We study entanglement-assisted quantum error-correcting codes (EAQECCs) arising from classical one-point algebraic geometry codes from the Hermitian curve with respect to the Hermitian inner product.
R. B. Christensen +3 more
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Machine learning line bundle connections
Physics Letters B, 2022 We study the use of machine learning for finding numerical hermitian Yang–Mills connections on line bundles over Calabi–Yau manifolds. Defining an appropriate loss function and focusing on the examples of an elliptic curve, a K3 surface and a quintic ...
Anthony Ashmore +3 more
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Weierstrass semigroup at m+1 rational points in maximal curves which cannot be covered by the Hermitian curve [PDF]
Des. Codes Cryptogr., 2020 We determine the Weierstrass semigroup $$H(P_\infty ,P_1,\ldots ,P_m)$$ at several rational points on the maximal curves which cannot be covered by the Hermitian curve introduced in Tafazolian et al.
A. Sepúlveda, M. Bras-Amorós
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Triples of rational points on the Hermitian curve and their Weierstrass semigroups [PDF]
Journal of Pure and Applied Algebra, 2020 In this paper, we study configurations of three rational points on the Hermitian curve over $\mathbb{F}_{q^2}$ and classify them according to their Weierstrass semigroups. For $q>3$, we show that the number of distinct semigroups of this form is equal to
Gretchen L. Matthews +2 more
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𝔽p2-maximal curves with many automorphisms are Galois-covered by the Hermitian curve
Advances in Geometry, 2021 Let 𝔽 be the finite field of order q2. It is sometimes attributed to Serre that any curve 𝔽-covered by the Hermitian curveHq+1:yq+1=xq+x ${{\mathcal{H}}_{q+1}}:{{y}^{q+1}}={{x }^{q}}+x$is also 𝔽-maximal.
D. Bartoli, M. Montanucci, F. Torres
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Deformations of Strong Kähler with torsion metrics
Complex Manifolds, 2021 Existence of strong Kähler with torsion metrics, shortly SKT metrics, on complex manifolds has been shown to be unstable under small deformations.
Piovani Riccardo, Sferruzza Tommaso
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An elementary abelian p-cover of the Hermitian curve with many automorphisms [PDF]
Mathematische Zeitschrift, 2020 The full automorphism group of a certain elementary abelian p-cover of the Hermitian curve in characteristic p>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy ...
H. Borges, Satoru Fukasawa
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