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Macaulay style formulas for toric residues

Published online by Cambridge University Press:  21 April 2005

Carlos D'Andrea  and
Amit Khetan
Carlos D'Andrea
Affiliation:
Miller Institute for Basic Research in Science and Department of Mathematics, University of California at Berkeley, Berkeley, CA 94720, USAcdandrea@math.berkeley.edu
Amit Khetan
Affiliation:
Department of Mathematics, University of California at Berkeley, Berkeley, CA 94720, USAkhetan@math.umass.edu Department of Mathematics, University of Massachusetts at Amherst, Amherst, MA 01002, USA
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Abstract

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We present an explicit formula for computing toric residues of ample divisors as a quotient of two determinants, à la Macaulay, where the numerator is a minor of the denominator. We present a combinatorial construction of a specific element of residue 1. We also give an irreducible representation of toric residues by extending the theory of subresultants to monomials of critical degree in the homogeneous coordinate ring of the corresponding toric variety.

Keywords

residuestoric varietiessubresultant14Q99
Type
Research Article
Information
Compositio Mathematica , Volume 141 , Issue 3 , May 2005 , pp. 713 - 728
Copyright
Foundation Compositio Mathematica 2005