Singular Curve Point Decompression Attack

2015 ◽  
Author(s):  
Johannes Blomer ◽  
Peter Gunther
Keyword(s):  
Singular Curve

Workspace of a Gimbal With Joint Limits

1996 ◽  
Author(s):  
Har-Jou Yeh ◽  
Karim A. Abdel-Malek
Keyword(s):  
Degrees Of Freedom ◽  
Spherical Surface ◽  
Perturbation Technique ◽  
Underlying Mechanism ◽  
Singular Curve ◽  
Constraint Function ◽  
Rank Deficiency ◽  
Analytical Criterion ◽  
Joint Limits ◽  
Three Degrees Of Freedom

Abstract An analytical formulation for determining the workspace of a point on a body suspended in a Gimbal mechanism is presented. Although the gimbal mechanism comprises three degrees of freedom, the resulting workspace is a region on a spherical surface. The constraint function of the underlying mechanism is studied for singularities using a row-rank deficiency condition of its constraint Jacobian. Singular curves on the resultant spherical surface are determined by a similar analytical criterion imposed on the system’s subjacobian, to compute a set of two joint singularities. These singular curves define regions on the spherical surface that may or may not be accessible. A perturbation technique is then used to identify singular curve segments that are boundary to the workspace region. The methodology is illustrated through a numerical example.

scholarly journals The hyperosculating spaces to certain curves in [n]

1975 ◽  
Vol 19 (3) ◽  
pp. 301-309 ◽  
Author(s):  
R. H. Dye
Keyword(s):  
Complete Intersection ◽  
Singular Curve ◽  
Classical Sense ◽  
Opposite Face

Let Γ be an irreducible and non-singular curve in [n] (n ≧ 3) which is the complete intersection of n − 1 primals of order m (m ≧ 2) with a common “self-polar” simplex S: by this I mean that the rth polar of each vertex of S with respect to any one of the defining primals is the opposite face of S counted m−r times, for r = 1, 2, …, m − 1. The various such Γ constitute the curves of the title; they were encountered in (2). When m = 2, Γ is the intersection of n − 1 quadrics with a common self-polar simplex in the familiar classical sense.

scholarly journals Jacobians of singular spectral curves and completely integrable systems

2000 ◽  
Vol 43 (3) ◽  
pp. 605-623 ◽  
Author(s):  
Olivier Vivolo
Keyword(s):  
Open Subset ◽  
Smooth Manifold ◽  
The Other ◽  
Completely Integrable Systems ◽  
Singular Curve ◽  
Generalized Jacobian ◽  
Zariski Open Subset ◽  
Spectral Curves ◽  
Multiple Eigenvalues ◽  
Leading Term

AbstractConsider an isospectral manifold formed by matrices M ∈ glr(ℂ)[x] with a fixed leading term. The description of such a manifold is well known in the case of a diagonal leading term with different eigenvalues. On the other hand, there are many important systems where this term has multiple eigenvalues. One approach is to impose conditions in the sub-leading term. The result is that the isospectral set is a smooth manifold, bi-holomorphic to a Zariski open subset of the generalized Jacobian of a singular curve.

scholarly journals ALBANESE VARIETIES OF CYCLIC COVERS OF THE PROJECTIVE PLANE AND ORBIFOLD PENCILS

2016 ◽  
Vol 227 ◽  
pp. 189-213
Author(s):  
E. ARTAL BARTOLO ◽  
J. I. COGOLLUDO-AGUSTÍN ◽  
A. LIBGOBER
Keyword(s):  
Projective Plane ◽  
Fundamental Group ◽  
Sufficient Conditions ◽  
Main Tool ◽  
Plane Curves ◽  
Abelian Surface ◽  
Singular Curve ◽  
Cyclic Covers ◽  
Genus 2 ◽  
Multiple Fibers

The paper studies a relation between fundamental group of the complement to a plane singular curve and the orbifold pencils containing it. The main tool is the use of Albanese varieties of cyclic covers ramified along such curves. Our results give sufficient conditions for a plane singular curve to belong to an orbifold pencil, that is, a pencil of plane curves with multiple fibers inducing a map onto an orbifold curve whose orbifold fundamental group is nontrivial. We construct an example of a cyclic cover of the projective plane which is an abelian surface isomorphic to the Jacobian of a curve of genus 2 illustrating the extent to which these conditions are necessary.

The postulation of a multiple curve

1942 ◽  
Vol 38 (4) ◽  
pp. 368-377
Author(s):  
B. Segre
Keyword(s):  
Continuous Variation ◽  
Intermediate Position ◽  
Singular Curve ◽  
Virtual Characters ◽  
Large Order

1. The postulation of a multiple curve for primals of sufficiently large order in space of any number of dimensions has been obtained recently by J. A. Todd, by a simple and elegant degeneration argument which, however, is not deemed to be a conclusive proof by the author himself. And, indeed, in order to make sure of the unconditional validity of such an argument, one should ascertain whether(i) the postulation θk of an irreducible non-singular curve ϲ, of order c and genus p, for the primals of sufficiently large order n of [r + 2] (r ≥ 1), required to go through it with multiplicity k (≥ 1), is a function of k, c, p, n, r only;(ii) it is possible, by means of a continuous variation of ϲ, to reduce this curve to connected polygon ϲ′ having the same virtual characters as ϲ, in such a way that each intermediate position of ϲ is still irreducible and non-singular;(iii) the postulation θk of ϲ equals the similarly defined postulation of ϲ′.

scholarly journals Euler potentials for the MHD Kamchatnov-Hopf soliton solution

2002 ◽  
Vol 9 (3/4) ◽  
pp. 347-354 ◽  
Author(s):  
V. S. Semenov ◽  
D. B. Korovinski ◽  
H. K. Biernat
Keyword(s):  
Numerical Simulations ◽  
Soliton Solution ◽  
Magnetic Helicity ◽  
Control Parameters ◽  
Singular Curve ◽  
Hopf Invariant ◽  
Special Programme

Abstract. In the MHD description of plasma phenomena the concept of magnetic helicity turns out to be very useful. We present here an example of introducing Euler potentials into a topological MHD soliton which has non-trivial helicity. The MHD soliton solution (Kamchatnov, 1982) is based on the Hopf invariant of the mapping of a 3-D sphere into a 2-D sphere; it can have arbitrary helicity depending on control parameters. It is shown how to define Euler potentials globally. The singular curve of the Euler potential plays the key role in computing helicity. With the introduction of Euler potentials, the helicity can be calculated as an integral over the surface bounded by this singular curve. A special programme for visualization is worked out. Helicity coordinates are introduced which can be useful for numerical simulations where helicity control is needed.

scholarly journals Elliptic Curves in Hyper-Kähler Varieties

2020 ◽  
Author(s):  
Denis Nesterov ◽  
Georg Oberdieck
Keyword(s):  
Elliptic Curves ◽  
Moduli Space ◽  
Modular Forms ◽  
Minimal Degree ◽  
Fano Variety ◽  
Singular Curve ◽  
Explicit Formulas

Abstract We show that the moduli space of elliptic curves of minimal degree in a general Fano variety of lines of a cubic four-fold is a non-singular curve of genus $631$. The curve admits a natural involution with connected quotient. We find that the general Fano contains precisely $3,780$ elliptic curves of minimal degree with fixed (general) $j$-invariant. More generally, we express (modulo a transversality result) the enumerative count of elliptic curves of minimal degree in hyper-Kähler varieties with fixed $j$-invariant in terms of Gromov–Witten invariants. In $K3^{[2]}$-type this leads to explicit formulas of these counts in terms of modular forms.

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