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Posted March 17, 2026
Last modified March 30, 2026

Algebra and Number Theory Seminar Questions or comments?

Shahriyar Roshan-Zamir, Tulane University
Interpolation in Weighted Projective Spaces

Over an algebraically closed field, the double point interpolation problem asks for the vector space dimension of the projective hypersurfaces of degree d singular at a given set of points. After being open for 90 years, a series of papers by J. Alexander and A. Hirschowitz in 1992--1995 settled this question in what is referred to as the Alexander-Hirschowitz theorem. In this talk, we primarily use commutative algebra to prove analogous statements in the weighted projective space, a natural generalization of the projective space. For example, we introduce an inductive procedure for weighted projective space, similar to that originally due to A. Terracini from 1915, to demonstrate an example of a weighted projective plane where the analogue of the Alexander-Hirschowitz theorem holds without exceptions and prove our example is the only such plane. Furthermore, Terracini's lemma regarding secant varieties is adapted to give an interpolation bound for an infinite family of weighted projective planes. There are no prerequisites for this talk besides some elementary knowledge of algebra.

Event contact: Gene Kopp