Arbitrary rank jumps for A-hypergeometric systems through Laurent polynomials Academic Article uri icon

abstract

  • We investigate the solution space of hypergeometric systems of differential equations in the sense of Gel'fand, Graev, Kapranov and Zelevinski. For any integer d 2, we construct a matrix A(d) d2d and a parameter vector (d) such that the holonomic rank of the A-hypergeometric system H A(d)((d)) exceeds the simplicial volume vol(A (d)) by at least d - 1. The largest previously known gap between rank and volume was 2. Our construction gives evidence to the general observation that rank jumps seem to go hand in hand with the existence of multiple Laurent (or Puiseux) polynomial solutions. 2007 London Mathematical Society.

published proceedings

  • JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES

author list (cited authors)

  • Matusevich, L. F., & Walther, U.

citation count

  • 2

complete list of authors

  • Matusevich, Laura Felicia||Walther, Uli

publication date

  • February 2007

publisher