Determinantal formula for the chow form of a toric surface

Authors:
Amit Khetan
Affiliations:
University of California at Berkeley, Berkeley, CA
Venue:
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Year:
2002

Citing 1
Cited 4

Hybrid sparse resultant matrices for bivariate systems

Proceedings of the 2001 international symposium on Symbolic and algebraic computation

Multihomogeneous resultant formulae by means of complexes

Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
The resultant of an unmixed bivariate system

Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Expressing a fraction of two determinants as a determinant

Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Bezoutian and quotient ring structure

Journal of Symbolic Computation

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Abstract

This paper gives an explicit method for computing the resultant of any sparse unmixed bivariate system with given support. We construct square matrices whose determinant is exactly the resultant. The matrices constructed are of hybrid Sylvester and Bézout type. Previous work by D'Andrea [6] gave pure Sylvester type matrices (in any dimension). In the bivariate case, D'Andrea and Emiris [8] constructed hybrid matrices with one Bézout row. These matrices are only guaranteed to have determinant some multiple of the resultant. The main contribution of this paper is the addition of new Bézout terms allowing us to achieve exact formulas. We make use of the exterior algebra techniques of Eisenbud, Fløystad, and Schreyer [10, 9].