The Probability-Resultant

Laughlin the Probability - Resultant

Transfinite Diameter and the Resultant

We prove a formula for the Fekete-Leja transfinite diameter of the pullback of a set E ⊂ C by a regular polynomial map F , expressing it in terms of the resultant of the leading part of F and the transfinite diameter of E. We also establish the nonarchimedean analogue of this formula. A key step in the proof is a formula for the transfinite diameter of the filled Julia set of F .

On the Height of the Sylvester Resultant

X iv :m at h/ 03 10 27 6v 2 [ m at h. N T ] 1 3 M ay 2 00 4 ON THE HEIGHT OF THE SYLVESTER RESULTANT CARLOS D’ANDREA AND KEVIN G. HARE Abstract. Let n be a positive integer. We consider the Sylvester resultant of f and g, where f is a generic polynomial of degree 2 or 3 and g is a generic polynomial of degree n. If f is a quadratic polynomial, we find the resultant’s height. If f is a cubic pol...

On the Newton Polytope of the Resultant

The study of Newton polytopes of resultants and discriminants has its orgin in the work of Gelfand, Kapranov, and Zelevinsky on generalized hypergeometric functions (see e.g., [8]). Central to this theory is the notion of the A-discriminant AA, which is the discriminant of a Laurent polynomial with specified support set A (see [6, 7]). Two main results of Gelfand, Kapranov, and Zelevinsky are c...

Dissolving the Puzzle of Resultant Moral Luck

The puzzle of resultant moral luck arises when we are disposed to think that an agent who caused a harm deserves to be blamed more than an otherwise identical agent who did not. One popular (but controversial) perspective on resultant moral luck explains our dispositions to produce different judgments with regard to the agents who feature in these cases as a product not of what they genuinely d...