The intersection of algebraic curves in three and higher dimensional spaces is considered. An algebrogeometric technique is developed for obtaining an upper bound on the number of intersection points of two irreducible algebraic curves. The asymptotic bounds are shown to be a function of only the degrees of the two intersecting curves. Some specific examples involving curves in 3-space are analyzed.
考虑了三维空间中的代数曲线的交点。为了获得两个不可约代数曲线的交点数目的上限,开发了一种代数几何技术。渐近边界显示为仅是两条相交曲线的度数的函数。分析了一些涉及3维曲线的具体例子。 P>
机译:分段代数曲线的实际相交点数的下界
机译:有界面尺寸较小时半空间相交的复杂度界
机译:有界面尺寸较小时半空间相交的复杂度界
机译:几个小次数代数方程组求解系统的多项式复杂度
机译:来自代数曲线的代码和秘密共享方案的改进边界。
机译:有限域上的代数复杂度和代数曲线
机译:$ W ^ r_d(C)$中的阿贝尔变体和代数曲线上的有界度点