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math.AG2020
Numerical homotopies from Khovanskii bases
Michael Burr, Frank Sottile, Elise Walker
We present numerical homotopy continuation algorithms for solving systems of equations on a variety in the presence of a finite Khovanskii basis. These take advantage of Anderson's…
math.AG2017
Serre's Properties for Quadratic Generated Domains from Graphs
Drew J. Lipman, Michael A. Burr
For any graph, one can construct a ring, called the edge ring, which is a quadratic-monomial generated subring of the Laurent polynomial ring . In…
math.AG2011
Asymptotic Purity for Very General Hypersurfaces of P^n x P^n of Bidegree (k,k)
Michael A. Burr
For a complex irreducible projective variety, the volume function and the higher asymptotic cohomological functions have proven to be useful in understanding the positivity of divi…