论文标题
在较高维空间中某些多芳基曲线曲线的二元性
Duality for certain multi-Frobenius nonclassical curves in higher dimensional spaces
论文作者
论文摘要
我们展示了特征$ p $的有限字段$ \ mathbb {f} _q $在其严格的双曲线的几何形状上反映出的曲线的多种曲线的多杂种非细胞。特别是，在这种情况下，我们可以描述其严格的双曲线与超平面线性系统的所有可能的相交多样性。除其他结果外，使用Homma的结果，我们能够构建非反射的空间曲线，使它们的切线表面也非反射性，并且Frobenius Map的通用点图像在其示意性超平面中。我们还获得了文献的一些已知结果的概括和改进。
We show how a type of multi-Frobenius nonclassicality of a curve defined over a finite field $\mathbb{F}_q$ of characteristic $p$ reflects on the geometry of its strict dual curve. In particular, in such cases we may describe all the possible intersection multiplicities of its strict dual curve with the linear system of hyperplanes. Among other consequence, using a result by Homma, we are able to construct nonreflexive space curves such that their tangent surfaces are nonreflexive as well, and the image of a generic point by a Frobenius map is in its osculating hyperplane. We also obtain generalizations and improvements of some known results of the literature.
