Mathematical Sciences: Algebraic Curves and Transverse Families

在这项研究中，Speiser将研究射影平面曲线，它们的对偶，以及一些将它们参数化的自然空间。计数问题，Tyrell关于非奇异三次曲线退化的猜想，以及关于任意特征的横截性的一般问题似乎密切相关，这将被研究。还将考虑具有给定数值特征的平面曲线的存在性的相关问题。首席研究员和他的合作者以及其他人在相关问题上的最新进展表明，这些问题的攻击线很有吸引力。

In this research Speiser will study projective plane curves, their duals, and some natural spaces which parametrize them. Enumerative problems, a conjecture of Tyrell about degenerations of nonsingular cubics, and general questions about transversality in arbitrary characteristic seem closely interconnected and this will be examined. A related problem about the existence of plane curves with given numerical characters will be considered, also. Recent progress on related questions by the principal investigator and his collaborators and others suggest attractive lines of attack for these problems.