Curves on Surfaces of Mixed Characteristic
نویسنده
چکیده
The classi cation of foliated surfaces, [McQ08], is applied to the study of curves on surfaces with big co-tangent bundle and varying moduli, be it purely in characteristic zero, or, more generally when the characteristic is mixed. Almost everything that one might naively imagine is true, but with one critical exception: rational curves on bi-disc quotients which aren't quotients of products of curves are Zariski dense in mixed characteristic. The logical repercussions in characteristic zero of this exception are not negligible.
منابع مشابه
Constructing Rational Curves on K3 Surfaces
We develop a mixed-characteristic version of the MoriMukai technique for producing rational curves on K3 surfaces. We reduce modulo p, produce rational curves on the resulting K3 surface over a finite field, and lift to characteristic zero. As an application, we prove that all complex K3 surfaces with Picard group generated by a class of degree two have an infinite number of rational curves.
متن کاملThe Curvature of Characteristic Curves on Surfaces
nalyzing and interrogating designed surfaces remains an important and widely researched issue in computer-aided geometric design (CAGD). Treating families of characteristic curves— such as contour lines, lines of curvature, asymptotic lines, isophotes, and reflection lines—on the surface proves a popular method of doing this. All these curves have something in common: s They reflect the surface...
متن کامل09 v 1 9 O ct 1 99 6 Hilbert - Kunz Functions of Cubic Curves and Surfaces
We determine the Hilbert-Kunz function of plane elliptic curves in odd characteristic, as well as over arbitrary fields the generalized Hilbert-Kunz functions of nodal cubic curves. Together with results of K. Pardue and P. Monsky, this completes the list of HilbertKunz functions of plane cubics. Combining these results with the calculation of the (generalized) Hilbert-Kunz function of Cayley’s...
متن کاملModelling of curves and surfaces in polarand
A new class of spline curves in polar coordinates has been presented in (SS anchez-Reyes, 1992) and independently considered in (de Casteljau, 1994). These are rational trigonometric curves in Cartesian coordinates and can be represented as NURBS. From the relationship existing with the correspondent curves in Cartesian coordinates an alternative way to derive some useful tools for modelling sp...
متن کاملTENSION QUARTIC TRIGONOMETRIC BÉZIER CURVES PRESERVING INTERPOLATION CURVES SHAPE
In this paper simple quartic trigonometric polynomial blending functions, with a tensionparameter, are presented. These type of functions are useful for constructing trigonometricB´ezier curves and surfaces, they can be applied to construct continuous shape preservinginterpolation spline curves with shape parameters. To better visualize objects and graphics atension parameter is included. In th...
متن کامل