Date: Tuesday, February 15, 2022
Location: 1360 East Hall (4:00 PM to 5:00 PM)
Title: BrillNoether theory over the Hurwitz space
Abstract: While in the 19th century an algebraic curve was synonymous with a onedimensional subset of projective space specified by polynomial equations, the modern study of curves makes use of the definition of an abstract curve independent of a projective embedding. BrillNoether theory is the bridge between these two perspectives. The fundamental question: given an abstract curve C, what is the geometry of the space of maps of C to projective space with certain invariants?
As a crowning achievement of the modern study of linear series in the 1980s, this geometry is wellunderstood when the curve C is sufficiently generic. However, in nature, curves are often encountered via a realization specified by polynomial equations of relatively small degree, which might force the curve to be too special for the classic BrillNoether theorem to apply. In this talk, I will discuss joint work with Eric Larson and Hannah Larson which provides the first complete analogue of all of the main theorems of BrillNoether theory when the curve is equipped with a low degree map to the line.
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Speaker: Isabel Vogt
Institution: Brown University
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