scholarly journals Obstructions to deforming curves on a 3-fold, III: Deformations of curves lying on a K3 surface

2017 ◽  
Vol 28 (13) ◽  
pp. 1750099 ◽  
Author(s):  
Hirokazu Nasu
Keyword(s):  
Elliptic Curves ◽  
Hilbert Scheme ◽  
Smooth Surface ◽  
Smooth Curve ◽  
K3 Surface ◽  
Sufficient Condition ◽  
Infinitesimal Deformation ◽  
First Order ◽  
Irreducible Components

We study the deformations of a smooth curve [Formula: see text] on a smooth projective [Formula: see text]-fold [Formula: see text], assuming the presence of a smooth surface [Formula: see text] satisfying [Formula: see text]. Generalizing a result of Mukai and Nasu, we give a new sufficient condition for a first order infinitesimal deformation of [Formula: see text] in [Formula: see text] to be primarily obstructed. In particular, when [Formula: see text] is Fano and [Formula: see text] is [Formula: see text], we give a sufficient condition for [Formula: see text] to be (un)obstructed in [Formula: see text], in terms of [Formula: see text]-curves and elliptic curves on [Formula: see text]. Applying this result, we prove that the Hilbert scheme [Formula: see text] of smooth connected curves on a smooth quartic [Formula: see text]-fold [Formula: see text] contains infinitely many generically non-reduced irreducible components, which are variations of Mumford’s example for [Formula: see text].

scholarly journals Incidence stratifications on Hilbert schemes of smooth surfaces, and an application to Poisson structures

2016 ◽  
Vol 27 (01) ◽  
pp. 1650006 ◽  
Author(s):  
Ziv Ran
Keyword(s):  
Poisson Structure ◽  
Hilbert Scheme ◽  
Smooth Surface ◽  
Smooth Curve ◽  
Smooth Surfaces ◽  
Poisson Structures ◽  
Hilbert Schemes ◽  
Hilbert Scheme Of Points

Given a smooth curve on a smooth surface, the Hilbert scheme of points on the surface is stratified according to the length of the intersection with the curve. The strata are highly singular. We show that this stratification admits a natural log-resolution, namely the stratified blowup. As a consequence, the induced Poisson structure on the Hilbert scheme of a Poisson surface has unobstructed deformations.

scholarly journals Higher rank Clifford indices of curves on a K3 surface

2021 ◽  
Vol 27 (3) ◽  
Author(s):  
Soheyla Feyzbakhsh ◽  
Chunyi Li
Keyword(s):  
Vector Bundles ◽  
Plane Curve ◽  
Smooth Curve ◽  
Line Bundles ◽  
K3 Surface ◽  
Clifford Index ◽  
Smooth Plane ◽  
Higher Rank ◽  
Rank Vector ◽  
Semistable Vector Bundle

AbstractLet (X, H) be a polarized K3 surface with $$\mathrm {Pic}(X) = \mathbb {Z}H$$ Pic ( X ) = Z H , and let $$C\in |H|$$ C ∈ | H | be a smooth curve of genus g. We give an upper bound on the dimension of global sections of a semistable vector bundle on C. This allows us to compute the higher rank Clifford indices of C with high genus. In particular, when $$g\ge r^2\ge 4$$ g ≥ r 2 ≥ 4 , the rank r Clifford index of C can be computed by the restriction of Lazarsfeld–Mukai bundles on X corresponding to line bundles on the curve C. This is a generalization of the result by Green and Lazarsfeld for curves on K3 surfaces to higher rank vector bundles. We also apply the same method to the projective plane and show that the rank r Clifford index of a degree $$d(\ge 5)$$ d ( ≥ 5 ) smooth plane curve is $$d-4$$ d - 4 , which is the same as the Clifford index of the curve.

ESTIMATING SURFACE NORMALS IN NOISY POINT CLOUD DATA

2004 ◽  
Vol 14 (04n05) ◽  
pp. 261-276 ◽  
Author(s):  
NILOY J. MITRA ◽  
AN NGUYEN ◽  
LEONIDAS GUIBAS
Keyword(s):  
Point Cloud ◽  
Smooth Surface ◽  
Smooth Curve ◽  
Local Information ◽  
Least Square ◽  
Neighborhood Size ◽  
Point Cloud Data ◽  
Cloud Data ◽  
Normal Estimation ◽  
Least Square Fitting

In this paper we describe and analyze a method based on local least square fitting for estimating the normals at all sample points of a point cloud data (PCD) set, in the presence of noise. We study the effects of neighborhood size, curvature, sampling density, and noise on the normal estimation when the PCD is sampled from a smooth curve in ℝ2or a smooth surface in ℝ3, and noise is added. The analysis allows us to find the optimal neighborhood size using other local information from the PCD. Experimental results are also provided.

scholarly journals Existence of nonoscillatory solutions of first order nonlinear neutral equations

1990 ◽  
Vol 32 (2) ◽  
pp. 180-192 ◽  
Author(s):  
Lu Wudu
Keyword(s):  
Nonoscillatory Solution ◽  
Sufficient Condition ◽  
Neutral Equation ◽  
Necessary And Sufficient Condition ◽  
Nonoscillatory Solutions ◽  
Neutral Equations ◽  
First Order ◽  
Image Position ◽  
Necessary And Sufficient

AbstractConsider the nonlinear neutral equationwhere pi(t), hi(t), gj(t), Q(t) Є C[t0, ∞), limt→∞hi(t) = ∞, limt→∞gj(t) = ∞ i Є Im = {1, 2, …, m}, j Є In = {1, 2, …, n}. We obtain a necessary and sufficient condition (2) for this equation to have a nonoscillatory solution x(t) with limt→∞ inf|x(t)| > 0 (Theorems 5 and 6) or to have a bounded nonoscillatory solution x(t) with limt→∞ inf|x(t)| > 0 (Theorem 7).

scholarly journals On B- Covariant Derivative of First Order for Some Tensors in different Spaces

2021 ◽  
Vol 2 (2) ◽  
pp. 30-37
Author(s):  
Alaa A. Abdallah ◽  
A. A. Navlekar ◽  
Kirtiwant P. Ghadle
Keyword(s):  
Curvature Tensor ◽  
Covariant Derivative ◽  
Torsion Tensor ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
First Order ◽  
Recurrence Property ◽  
Necessary And Sufficient ◽  
The Relationship

In this paper, we study the relationship between Cartan's second curvature tensor $P_{jkh}^{i}$ and $(h) hv-$torsion tensor $C_{jk}^{i}$ in sense of Berwald. Moreover, we discuss the necessary and sufficient condition for some tensors which satisfy a recurrence property in $BC$-$RF_{n}$, $P2$-Like-$BC$-$RF_{n}$, $P^{\ast }$-$BC$-$RF_{n}$ and $P$-reducible-$BC-RF_{n}$.

scholarly journals Complete intersections primitive structures on space curves

2015 ◽  
Vol 26 (12) ◽  
pp. 1550104
Author(s):  
Philippe Ellia
Keyword(s):  
Complete Intersection ◽  
Smooth Surface ◽  
Smooth Curve ◽  
Complete Intersections ◽  
Multiple Structure ◽  
Space Curves ◽  
Structure Formula ◽  
Primitive Structure

A multiple structure [Formula: see text] on a smooth curve [Formula: see text] is said to be primitive if [Formula: see text] is locally contained in a smooth surface. We give some numerical conditions for a curve [Formula: see text] to be a primitive set theoretical complete intersection (i.e. to have a primitive structure which is a complete intersection).

A SUFFICIENT CONDITION FOR THE UNIQUENESS OF NORMAL FORMS AND UNIQUE NORMAL FORMS OF GENERALIZED HOPF SINGULARITIES

2004 ◽  
Vol 14 (09) ◽  
pp. 3337-3345 ◽  
Author(s):  
JIANPING PENG ◽  
DUO WANG
Keyword(s):  
Normal Form ◽  
Normal Forms ◽  
Sufficient Condition ◽  
First Order ◽  
Recursive Formulas ◽  
Unique Normal Forms

A sufficient condition for the uniqueness of the Nth order normal form is provided. A new grading function is proposed and used to prove the uniqueness of the first-order normal forms of generalized Hopf singularities. Recursive formulas for computation of coefficients of unique normal forms of generalized Hopf singularities are also presented.

scholarly journals On the decomposition of the small diagonal of a K3 surface

2019 ◽  
Vol 19 (3) ◽  
pp. 353-358
Author(s):  
Ivan Bazhov
Keyword(s):  
Elliptic Curves ◽  
K3 Surface ◽  
The One

Abstract We give a new proof of the theorem of Beauville and Voisin about the decomposition of the small diagonal of a K3 surface S. Our proof is explicit and works with the embedding of S in ${\mathbb P}^g$ . It is different from the one used by Beauville and Voisin, which employed the existence of one-parameters families of elliptic curves

Sign in / Sign up

Export Citation Format

Share Document