Mathematical Sciences: Algebraic Curves and Transverse Families

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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.