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A hands-on approach to tensor product surfaces of bidegree (2,1)

Banff International Research Station for Mathematical Innovation and Discovery

A central problem in geometric modeling is to find the implicit equations for a curve or surface defined by a regular or rational map. For surfaces the two most common situations are when the surface is given by a map \(\mathbb{P}^1\times \mathbb{P}^1 \to \mathbb{P}^3\) or \(\mathbb{P}^2 \to \mathbb{P}^3\). The image of regular map \(\mathbb{P}^1\times \mathbb{P}^1 \to \mathbb{P}^3\) is called a tensor product surface. We study singularities of tensor product surfaces parametrized by polynomials of bidegree (2, 1) in relation to the syzygies of the ideal generated by these polynomials. We determine all possible numerical types of bigraded minimal free resolutions of such an ideal. This is based on joint work with Hal Schenck and Javid Validashti.

Mathematics; Algebraic geometry; Computer science; Applied computer science

video/mp4

Author affiliation: University of Nebraska

2017-02-09

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60539

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/