Mathematical Sciences: Algebraic Curves and Transverse Families

在本研究中，Speiser将研究射影平面曲线，它们的对偶，以及一些参数化它们的自然空间。列举问题，提勒尔关于非奇异立方体退化的猜想，以及关于任意特征的横向性的一般问题似乎密切相关，这将被研究。此外，还将讨论具有给定数值特征的平面曲线的存在性问题。首席研究员及其合作者和其他人在相关问题上的最新进展为这些问题提供了有吸引力的攻击路线。

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.