Related papers: Interpolation for Brill-Noether space curves

Let N_d be the number of degree d, nodal, rational plane curves through 3d-1 points in the complex projective plane. The number of degree d>=3, nodal, elliptic plane curves with a fixed (general) j-invariant through 3d-1 points is found to…

We study the mean dimensions of the spaces of Brody curves. In particular we give the formula of the mean dimension of the space of Brody curves in the Riemann sphere.

Mukai showed that projective models of Brill-Noether general polarized K3 surfaces of genus $6-10$ and $12$ are obtained as linear sections of projective homogeneous varieties, and that their hyperplane sections are Brill-Noether general…

Fix a non-square integer $k\neq 0$. We show that the number of curves $E_B:y^2=x^3+kB^2$ containing an integral point, where $B$ ranges over positive integers less than $N$, is bounded by $O_k(N(\log N)^{-\frac{1}{2}+\epsilon})$. In…

A Brill-Noether degeneracy locus is closure in $\Pic^d(C)$ of the locus of line bundles with a specified rank function $r(a,b) = h^0(C,L(-ap-bq))$. These loci generalize the classical Brill-Noether loci $W^r_d(C)$ as well as Brill-Noether…

We prove that for a sufficiently ample line bundle $L$ on a surface $S$, the number of $\delta$-nodal curves in a general $\delta$-dimensional linear system is given by a universal polynomial of degree $\delta$ in the four numbers…

In this paper we study the Brill Noether locus of rank 2, (semi)stable vector bundles with at least two sections and of suitable degrees on a general $\nu$-gonal curve. We classify its reduced components whose dimensions are at least the…

We present a method to compute the magnification of a finite source star lensed by a triple lens system based on the image boundary (contour integration) method. We describe a new procedure to obtain continuous image boundaries from…

We completely describe the Brill-Noether theory for curves in the primitive linear system on generic abelian surfaces, in the following sense: given integers $d$ and $r$, consider the variety $V^r_d(|H|)$ parametrizing curves $C$ in the…

This work provides a complete characterization of the solutions of a linear interpolation problem for vector polynomials. The interpolation problem consists in finding n scalar polynomials such that an equation involving a linear…

Particle tracing through numerical integration is a well-known approach to generating pathlines for visualization. However, for particle simulations, the computation of pathlines is expensive, since the interpolation method is complicated…

We give a formula for the number of interior intersection points made by the diagonals of a regular $n$-gon. The answer is a polynomial on each residue class modulo 2520. We also compute the number of regions formed by the diagonals, by…

In this paper, we will give a uniform upper bound of the number of rational points of bounded height in non-singular curves by applying the global determinant method.

For a smooth plane cubic $B$, we count curves $C$ of degree $d$ such that the normalizations of $C\backslash B$ are isomorphic to $\Bbb A^1$, for $d\leq7$ (for $d=7$ under some assumption). We also count plane rational quartic curves…

For affine algebraic plane curves we reduce a calculation of its invariants to calculation of the intersection of kernels of some derivations.

We present a condition number of the intersection of two B\'ezier curves.

In this paper, we present a probabilistic algorithm to compute the number of $\mathbb{F}_p$-points of modular curve $X_1(n)$. Under the Generalized Riemann Hypothesis(GRH), the algorithm takes…

We obtain a sharp bound on the number of self-intersections of a closed planar curve with trigonometric parameterization. Moreover, we show that a generic curve of this form is normal in the sense of Whitney.

Using the Semple bundle construction, we derive an intersection-theoretic formula for the number of simultaneous contacts of specified orders between members of a generic family of degree $d$ plane curves and finitely many fixed curves. The…

Given two general rational curves of the same degree in two projective spaces, one can ask whether there exists a third rational curve of the same degree that projects to both of them. We show that, under suitable assumptions on the degree…