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On Some Components of Hilbert Schemes of Curves
Let \(\mathcal {I}_{d,g,R}\) be the union of irreducible components of the...
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Counting elliptic curves over the rationals with a 7-isogeny
We count by height the number of elliptic curves over the rationals, both up to isomorphism over the rationals and over an algebraic closure thereof,...
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Constructing local controlled developable H-Bézier surfaces by interpolating characteristic curves
The developable surface is always a hot issue in CAGD, CAD/CAM and used in many manufacturing planning operations, e.g., for ships, aircraft wing,...
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Cubic and Quartic Space Curves as Intersections of Quadrics
Quartic space of curves q of the second kind are part of the intersection of a quadric Q and a cubic surface C which share two further straight lines...
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Exact Solutions and Dynamical Behaviors of the Raman Soliton Model with Anti-Cubic Nonlinearity
This work investigates the exact solutions of the Raman soliton model with anti-cubic nonlinear in optical metamaterials. By travelling wave...
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On signatures of elliptic curves and modular forms
In [
4 ], the first and second authors studied the signatures of Dirichlet characters and elliptic curves. In this paper we improve their lower bound... -
Riemannian Stochastic Variance-Reduced Cubic Regularized Newton Method for Submanifold Optimization
We propose a stochastic variance-reduced cubic regularized Newton algorithm to optimize the finite-sum problem over a Riemannian submanifold of the...
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Applications of the Fundamentals of Bézier Curves
This study presents applications of Bézier curves as design and analysis tools in two engineering study cases. In the first case, different types of...
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Remarks on double points of plane curves
We study the relation between the type of a double point of a plane curve and the curvilinear 0-dimensional subschemes of the curve at the point. An...
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Non-reduced Components of the Hilbert Scheme of Curves Using Triple Covers
In this paper, we consider curves on a cone that pass through the vertex and are also triple covers of the base of the cone, which is a general...
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Curves Are Surfaces
The implicit function theorem allows us to define an atlas for a nonsingular complex curve which makes it a Riemann surface. This structure is used...
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Prelog Chow groups of self-products of degenerations of cubic threefolds
It is unknown whether smooth cubic threefolds have an (integral Chow-theoretic) decomposition of the diagonal, or whether they are stably rational or...
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Higher Genus FJRW Theory for Fermat Cubic Singularity
In this paper, we study the higher genus FJRW theory of Fermat cubic singularity with maximal group of diagonal symmetries using Givental formalism....
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