Related papers: Subvarieties of low degree on general hypersurface…
We consider smooth codimension two subcanonical subvarieties in $\mathbb{P}^n$ with $n \geq 5$, lying on a hypersurface of degree $s$ having a linear subspace of multiplicity $(s-2)$. We prove that such varieties are complete intersections.…
Classically, the projective duality between joins of varieties and the intersections of varieties only holds in good cases. In this paper, we show that categorically, the duality between joins and intersections holds in the framework of…
We explore a novel method to generate and characterize complex networks by means of their embedding on hyperbolic surfaces. Evolution through local elementary moves allows the exploration of the ensemble of networks which share common…
This note is a survey on the topology of hyperplane arrangements. We mainly focus on the relationship between topology and the real structure, such as adjacent relations of chambers and stratifications related to real structures.
This is an expanded version of the two papers "Interpolation of Varieties of Minimal Degree" and "Interpolation Problems: Del Pezzo Surfaces." It is well known that one can find a rational normal curve in $\mathbb P^n$ through $n+3$ general…
The first part of this paper considers higher order CR invariants of three dimensional hypersurfaces of finite type. Using a full normal form we give a complete characterization of hypersurfaces with trivial local automorphism group, and…
A very interesting problem in the classical theory of minimal surfaces consists of the classification of such surfaces under some geometrical and topological constraints. In this short paper, we give a brief summary of the known…
We consider various equivalence relations on the set of homotopy classes of curves on a hyperbolic surface based on topological, algebraic, and geometric structures. The purpose of this work is to determine the relationship between these…
This is a continuation of "Rational curves on hypersurfaces of low degree", math.AG/0203088. We prove that if d^2+d+1 < n and d > 2, then for a general hypersurface X_d in P^n of degree d, for each degree e the space of rational curves of…
In this paper, we consider holomorphic mappings between real hypersurfaces in different dimensional complex spaces. We give a number of conditions that imply that such mappings are transversal to the target hypersurface at most points.
Our goal is to give Schmidt's subspace theorem for moving hypersurface targets in subgeneral position in projective varieties.
We analyze single particle coherence and interference in the presence of particle loss and derive an inequality that relates the preservation of coherence, the creation of superposition with the vacuum, and the degree of particle loss. We…
In this paper, we prove a generalization of the Schmidt's subspace theorem for polynomials of higher degree in subgeneral position with respect to a projective variety over a number field. Our result improves and generalizes the previous…
This is a brief and gentle introduction, aimed at graduate students, to the subject of model subspaces of the Hardy space.
The purpose of this note is to prove Grothendieck's standard conjectures for the Fano variety of lines on a smooth cubic hypersurface in projective space.
Characterization of topology and dimensionality of spectral feature spaces provides insight into information content. The objective of this study is to characterize topology and spectral dimensionality of spectral mixing spaces representing…
An open set in C^n is pseudoconvex if and only if its intersection with every affine subspace of complex dimension two as seen as an open set in C^2 is pseudoconvex.
One of the themes in algebraic geometry is the study of the relation between the ``topology'' of a smooth projective variety and a (``general'') hyperplane section. Recent results of Nori produce cohomological evidence for a conjecture that…
We prove analogues of several well-known results concerning rational morphisms between quadrics for the class of so-called quasilinear $p$-hypersurfaces. These hypersurfaces are nowhere smooth over the base field, so many of the geometric…
This paper gives, in generic situations, a complete classification of ruled minimal surfaces in pseudo-Euclidean space with arbitrary index. In addition, we discuss the condition for ruled minimal surfaces to exist, and give a…