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4 papers · 1 filter
Polynomial recurrences and cyclic resultants
Christopher J. Hillar, Lionel Levine
Let be an algebraically closed field of characteristic zero and let . The -th {\it cyclic resultant} of is \[r_m = \text{Res}(f,x^m-1).\] A generic monic pol…
Elementary modifications and line configurations in P^2
Henry K. Schenck
Associated to an arrangement of projective hyperplanes A is the module D(A), which consists of derivations tangent to A. We study D(A) when A is a configuration of lines in the pro…
Algebraic Geometry of Bayesian Networks
Luis David Garcia, Michael Stillman, Bernd Sturmfels
We study the algebraic varieties defined by the conditional independence statements of Bayesian Networks. A complete algebraic classification is given for Bayesian Networks on at m…
Counting Real Connected Components of Trinomial Curve Intersections and m-nomial Hypersurfaces
Tien-Yien Li, J. Maurice Rojas, Xiaoshen Wang
We prove that any pair of bivariate trinomials has at most 5 isolated roots in the positive quadrant. The best previous upper bounds independent of the polynomial degrees were much…