Related papers: Unexpected hypersurfaces with multiple fat points
We complete the classification of ruled real hypersurfaces with shape operator of constant norm in nonflat complex space forms by showing the existence of a unique inhomogeneous example in the complex hyperbolic space.
We establish a near dichotomy between randomness and structure for the point counts of arbitrary projective cubic threefolds over finite fields. Certain "special" subvarieties, not unlike those in the Manin conjectures, dominate. We also…
An exceptional point is a special point in parameter space at which two (or more) eigenvalues and eigenvectors coincide. The discovery of exceptional points within mechanical and optical systems has uncovered peculiar effects in their…
The study of non-Hermitian degeneracies -- called exceptional points -- has become an exciting frontier at the crossroads of optics, photonics, acoustics, and quantum physics. Here, we introduce the Newton polygon method as a general…
In this paper, we compute the number of real forms of Fermat hypersurfaces for degree $d \ge 2$ except the degree 4 surface case, and give explicit descriptions of them.
Unconventional Weyl points with topological charges higher than 1 can transform into various complex unconventional Weyl exceptional contours under non-Hermitian perturbations. However, theoretical studies of these exceptional contours have…
Let $\mathbb{F}_q$ be a finite field with $q=p^n$ elements. In this paper, we study the number of $\mathbb{F}_q$-rational points on the affine hypersurface $\mathcal X$ given by $a_1 x_1^{d_1}+\dots+a_s x_s^{d_s}=b$, where…
The object of this paper is to introduce new classes of hypersurfaces of almost product-like statistical manifolds. The main properties and relations on $K-$para contact, para cosymplectic, para Sasakian and conformal hypersurfaces are…
In this paper, we prove the short-time existence of hyperbolic inverse (mean) curvature flow (with or without the specified forcing term) under the assumption that the initial compact smooth hypersurface of $\mathbb{R}^{n+1}$…
We verify that elliptic K3 surfaces and algebraic groups have many rational points over function fields, i.e., they are geometrically special in the sense of Javanpeykar-Rousseau. We also show that under additional assumptions, this…
The theoretical computing of special values assumed by the hypergeometric functions has a high interest not only on its own, but also in sight of the remarkable implications to both pure Mathematics and Mathematical Physics. Accordingly, in…
Non-Hermitian systems exhibit interesting band structures, where novel topological phenomena arise from the existence of exceptional points at which eigenvalues and eigenvectors coalesce. One important open question is how this would…
Unconventional fermions, such as three-fold, four-fold, six-fold, and eight-fold fermions have attracted intense attention in recent years. However, the concrete materials hosting unconventional fermions are still in urgent scarcity. In…
The Euler characteristic of a very affine variety encodes the number of critical points of the likelihood equation on this variety. In this paper, we study the Euler characteristic of the complement of a hypersurface arrangement with…
We prove that in a closed Riemannian manifold with dimension between $3$ and $7$, either there are minimal hypersurfaces with arbitrarily large area, or there exist uncountably many stable minimal hypersurfaces. Moreover, the latter case…
In the first part of this paper, we establish some results around generalized Borel's Theorem. As an application, in the second part, we construct example of smooth surface of degree $d\geq 19$ in $\mathbb{CP}^3$ whose complements is…
In this paper, we investigate Einstein hypersurfaces of the warped product $I\times_{f}\mathbb{Q}^{n}(c)$, where $\mathbb{Q}^{n}(c)$ is a space form of curvature $c$. We prove that $M$ has at most three distinct principal curvatures and…
The non-Hermitian skin effect, characterized by a proliferation of exponentially localized edge modes in open-boundary systems, has led to the discovery of numerous novel physical phenomena that challenge the limits of conventional band…
The author has been interested in regions surrounded by cylinders of real algebraic hypersurfaces and their shapes and polynomials associated to them. Here, we formulate and investigate natural decompositions into such cylinders of real…
Problems with localized nonhomogeneous material properties arise frequently in many applications and are a well-known source of difficulty in numerical simulations. In certain applications (including additive manufacturing), the physics of…