# liftMatrixToEN -- Lifts a matrix between bundles on the scroll to the associated Eagon-Northcott type complexes

## Synopsis

• Usage:
A=liftMatrixToEN(Psi,e)
• Inputs:
• Psi, , the matrix that defines map between vector bundles on the scroll.
• e, a list, the type of the scroll $P(E)$
• Outputs:
• A, , the induced map

## Description

Given a map between vector bundles F and G on a normalized scroll of type e, this function computes the induced map between the first modules in the Eagon-Northcott type resolution of F and G.

 i1 : (g,k,n) = (8,5,1000) o1 = (8, 5, 1000) o1 : Sequence i2 : e = balancedPartition(k-1,g-k+1) o2 = {1, 1, 1, 1} o2 : List i3 : Ican = canCurveWithFixedScroll(g,k,n); ZZ o3 : Ideal of ----[t ..t ] 1009 0 7 i4 : Jcan = curveOnScroll(Ican,g,k); ZZ o4 : Ideal of ----[pp ..pp , v..w] 1009 0 3 i5 : betti(resX = resCurveOnScroll(Jcan,g,2)) 0 1 2 3 o5 = total: 1 5 5 1 0: 1 . . . 1: . . . . 2: . 4 1 . 3: . 1 4 . 4: . . . . 5: . . . 1 o5 : BettiTally i6 : betti(liftMatrixToEN(resX.dd_1,e)) 0 1 o6 = total: 1 9 0: 1 . 1: . 9 o6 : BettiTally i7 : betti(liftMatrixToEN(resX.dd_2,e)) 0 1 o7 = total: 9 11 2: 9 11 o7 : BettiTally i8 : betti(liftMatrixToEN(resX.dd_3,e)) 0 1 o8 = total: 11 3 3: 11 . 4: . 3 o8 : BettiTally