eagonNorthcottType -- Computes the Eagon-Northcott type resolution

Synopsis

• Usage:
resX=resCurveOnScroll(Phi,b)
• Inputs:
• Phi, , the matrix whose maximal minors define the scroll
• b, an integer, the twist
• Outputs:
• ENresolution, , the Eagon-Northcott type resolution

Description

This function computes the Eagon-Northcott type resolution associated to the matrix Phi defining the scroll and an integer b defining the twist $O_{P(E)}(bR)$. The way the function works is similar to the way the "Eagon-Northcott" function by Greg Smith works.

 i1 : R = ZZ/12347[x_0..x_7] o1 = R o1 : PolynomialRing i2 : Phi = matrix{{x_0..x_3},{x_4..x_7}} o2 = | x_0 x_1 x_2 x_3 | | x_4 x_5 x_6 x_7 | 2 4 o2 : Matrix R <--- R i3 : betti(eagonNorthcottType(Phi,0)) 0 1 2 3 o3 = total: 1 6 8 3 0: 1 . . . 1: . 6 8 3 o3 : BettiTally i4 : betti(eagonNorthcottType(Phi,1)) 0 1 2 3 o4 = total: 2 4 4 2 0: 2 4 . . 1: . . 4 2 o4 : BettiTally