Article
Mathematics
Momonari Kudo, Shushi Harashita
Summary: This paper presents an algorithm to enumerate superspecial trigonal curves of genus 5 for arbitrary q, and the algorithm is implemented using the computer algebra system Magma. The computational results obtained by the implementation are used to prove the existence or nonexistence of such curves for specific q values, and to determine the number of isomorphism classes of curves with explicit defining equations for q = 11.
EXPERIMENTAL MATHEMATICS
(2022)
Article
Mathematics
Valentina Beorchia, Gian Pietro Pirola, Francesco Zucconi
Summary: This study focuses on infinitesimal deformations of a trigonal curve preserving trigonal series and Hodge structure of rank 1. It proves that under certain conditions, such loci are zero-dimensional and completes a prior result, ultimately concluding the uniqueness of the hyperelliptic locus in the moduli space of curves of genus g.
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
(2021)
Article
Mathematics
Ji Guo, Chia-Liang Sun, Julie Tzu-Yueh Wang
Summary: We first establish the second main theorem for algebraic tori with slow growth moving targets with truncation to level 1 and apply it to prove the Green-Griffiths-Lang conjecture for projective spaces with n+1 components in the context of moving targets of slow growth. Then, we discuss the integrability of the ring of exponential polynomials in the ring of entire functions as another application.
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
(2022)
Article
Mathematics
Anand Deopurkar, Changho Han
Summary: This article explicitly describes the KSBA/Hacking compactification of a moduli space of log surfaces of Picard rank 2, proving that the compactified moduli space is a smooth Deligne-Mumford stack with 4 boundary components. It is related to the moduli space of genus 4 curves and the compactification of the Hurwitz space of triple coverings of P-1 by genus 4 curves.
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
(2021)
Article
Engineering, Mechanical
Yanwei Han, Zijian Zhang
Summary: The traditional Watt's centrifugal governors face challenges in both model design and analytical approach. However, little attention has been focused on the development of a new model and control scheme for the centrifugal governor system. This study presents a novel three-dimensional differential equation model for the trigonal centrifugal governor, introduces new-style nonlinearities, and examines various dynamical behaviors. The experimental setup verifies the theoretical analysis and numerical findings, indicating potential applications in mechanical engineering and control systems.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Applied
Kuwari Mahanta, Sreekrishna Palaparthi
Summary: This paper studies the curve graph of closed, orientable surfaces and demonstrates that under certain conditions, if two vertices are at a distance of 3, a third vertex corresponds to distances 4 and 3 from these two vertices. This provides many tractable examples of distance 4 vertices in the curve graph and establishes an upper bound for the minimum intersection number of curves at a distance of 4.
TOPOLOGY AND ITS APPLICATIONS
(2022)
Article
Mathematics, Interdisciplinary Applications
Juncheng Li, Chengzhi Liu
Summary: This paper presents algorithms for smoothing two connected ball Bezier curves by minimizing the energies of the curves, which have been proven effective through numerical examples.
Article
Astronomy & Astrophysics
Lachlan G. Bishop, Timothy C. Ralph, Fabio Costa
Summary: Past studies on the billiard-ball paradox have focused on classical histories, while this study develops a quantum version using a quantum circuit to describe various paths. The model finds self-consistent solutions using Deutsch's prescription and pure-state solutions using the postselected teleportation prescription. The study also discusses methods for ensuring convergence in the continuum limit.
CLASSICAL AND QUANTUM GRAVITY
(2022)
Article
Mathematics
Antonio Alarcon
Summary: In this paper, it is proven that each smooth complete closed complex hypersurface in the open unit ball B^n of C^n is a level set of a noncritical holomorphic function on B^n, leading to a nonsingular holomorphic foliation. A more general result is also established for complex submanifolds, with the existence of a nonsingular holomorphic submersion foliation of B^n by smooth complete closed complex submanifolds of any pure codimension q in {1, . . . , n-1}.
JOURNAL OF DIFFERENTIAL GEOMETRY
(2022)
Article
Mathematics
Yota Maeda
Summary: We study the branch divisors on the boundary of the canonical toroidal compactification of ball quotients. We show a criterion, the low slope cusp form trick, for proving that ball quotients are of general type. Moreover, we classify when irregular cusps exist in the case of the discriminant kernel and construct concrete examples for some arithmetic subgroups. As another direction of study, when a complex ball is embedded into a Hermitian symmetric domain of type IV, we determine when regular or irregular cusps map to regular or irregular cusps studied by Ma.
MATHEMATISCHE NACHRICHTEN
(2023)
Article
Mathematics
Gavril Farkas, Alessandro Verra
Summary: By utilizing the connection found by Hassett between the Noether-Lefschetz moduli space C-42 of special cubic fourfolds of discriminant 42 and the moduli space F-22 of polarized K3 surfaces of genus 22, it is shown that the universal K3 surface over F-22 is unirational.
MATHEMATISCHE ANNALEN
(2021)
Article
Computer Science, Artificial Intelligence
Gang Hu, Wanting Dou, Guo Wei, Muhammad Abbas
Summary: In this paper, an improved chimp optimization algorithm (ICHOA) is used to solve the multi-degree reduction problem of ball Said-Ball curves (BSB curves) in computer aided design (CAD) and computer graphics (CG). The ICHOA algorithm, combined with proportional weight, dimension learning-based hunting search, and fractional order strategies, is developed to improve the calculation accuracy and the ability to avoid local minima. Experimental results demonstrate the effectiveness of the proposed ICHOA in solving the optimization problems of multi-degree reduction of BSB curves.
ARTIFICIAL INTELLIGENCE REVIEW
(2023)
Article
Mathematics
Emily Clader, Felix Janda, Yongbin Ruan, Yang Zhou
Summary: This paper introduces a technique for proving wall-crossing formulas in the gauged linear sigma model, without assuming factorization properties of the virtual class. Applying this technique to the gauged linear sigma model associated to a complete intersection in weighted projective space, a uniform proof of the wall-crossing formula in both the geometric and the Landau-Ginzburg phase is obtained.
DUKE MATHEMATICAL JOURNAL
(2021)
Article
Physics, Mathematical
Yongbin Ruan, Yingchun Zhang, Jie Zhou
Summary: In this paper, we first formulate theories of differential rings for Siegel quasi-modular and Siegel quasi-Jacobi forms for genus two. Then, we apply these theories to the Eynard-Orantin topological recursion of the toric Calabi-Yau threefold C-3/Z(6) with a brane whose mirror curve is a genus-two hyperelliptic curve. By proving the Remodeling Conjecture, we show that the open- and closed- Gromov-Witten potentials of this system are essentially Siegel quasi-Jacobi and Siegel quasi-modular forms for genus two, respectively.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2023)
Article
Mathematics
Takeshi Abe
Summary: The article demonstrates that any zero-dimensional subvariety of a very general degree d hypersurface X⊂Pn with geometric genus zero can be expressed as a union of lines and conics. Specifically, any rational curve on X⊂Pn is a line or a conic if d > 51 (7n + 16).
ALGEBRAIC GEOMETRY
(2023)
