Seminar
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| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
Interpolation in the weighted projective space
Given a finite set of points X in the projective space over a field k one can ask for the k-vector space dimension of all degree d polynomials that vanish to order two on X. (These are polynomials whose first derivative vanishes on X.) The Alexander-Hirschowitz theorem (A-H) computes this dimension in terms of the multiplicity of the points and the k-vector space dimension of degree d monomials, with finitely many exceptions. In this talk, we investigate this question in the weighted projective line and space, P(s, t) and P(a, b, c). We define a notion of multiplicity for weighted projective spaces, give an example of P(a, b, c) where A-H holds with no exceptions and an infinite family where A-H fails for even one point, and discuss future directions.
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