相关论文: Spin curves over non-stable curves
We carry out a survey on curves defined over finite fields that are Diophantine stable; that is, with the property that the set of points of the curve is not altered under a proper field extension. First, we derive some general results of…
In this paper, we survey recent developments concerning the stability of naturally defined bundles on curves that play a central role in the deformation theory of the curve.
Non-orientable nanostructures are becoming feasable today. This lead us to the study of spin in these geometries. Hence a physically sound definition of spin is suggested. Using our definition, we study the question of the number of…
We give a classification and a construction of all smooth $(n-1)$-dimensional varieties of lines in ${\bf P}\sp n$ verifying that all their lines meet a curve. This also gives a complete classification of $(n-1)$-scrolls over a curve…
The main result of this article is that the component of the Alexeev-Koll\'{a}r-Shepherd-Barron moduli space of stable surfaces parameterizing stable degenerations of symmetric squares of curves is isomorphic to the moduli space of stable…
The geometry of the moduli space of stable spin curves is studied, with emphasis on its combinatorial properties. In this context, the standard graph theoretic framework is not just a book-keeping device: some purely combinatorial results…
We observe that if we are interested primarily in degeneration arguments, there is a weaker notion of (semi)stability for vector bundles on reducible curves, which is sufficient for many applications, and does not depend on a choice of…
We give a sharp bound on the number of automorphisms of a stable curve of a given genus and describe all curves attaining this bound.
The aim of this paper is to investigate the sufficient condition for the invariance of a normal curve on a smooth immersed surface under isometry. We also find the the deviations of the tangential and normal components of the curve with…
Boundary points on the moduli space of pointed curves corresponding to collisions of marked points have modular interpretations as degenerate curves. In this paper, we study degenerations of orbifold projective curves corresponding to…
For curves singularities the dimension of smoothing components in the deformation space is an invariant of the singularity, but in general the deformation space has components of different dimensions. We are interested in the question what…
We study the deformation of $G$-marked stable curves in the case where $G$ is a cyclic group, and construct a parameterizing space for $G$-marked stable curves of a given numerical type. This is then used in order to study the components of…
We study the relationship between the smoothness of a plane curve and that of its evolute, especially in the cases where the parent curve is no more two or three times continuously differentiable, and exhibit the same kind of apparent…
We define a new finite type invariant for stably homeomorphic class of curves on compact oriented surfaces without boundaries and extend to a regular homotopy invariant for spherical curves.
We give an explicit construction of a closed curve with constant torsion and everywhere positive curvature. We also discuss the restrictions on closed curves of constant torsion when they are constrained to lie on convex surfaces.
The well known formulas express the curvature and the torsion of a curve in $R^3$ in terms of euclidean invariants of its derivatives. We obtain expressions of this kind for all curvatures of curves in $R^n$. It follows that a curve in…
The briefly review on the common spin description of the nonlinear evolution equations.
We investigate numerically in spherical geometry the interaction of stratification with precession. Both stable stratification and unstable stratification are studied. In the parameter regime we are concerned with, stable stratification…
We introduce a notion of limit linear series for nodal curves which are not of compact type. We give a construction of a moduli space of limit linear series, which works also in smoothing families, and we prove a corresponding…
We introduce and consider the notion of stable degeneracies of translation invariant energy functions for finite Ising models. By this term we mean the lack of injectivity that cannot be lifted by changing the interaction. We show that…