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VectorBundleOnE -- vector bundle on a hyperelliptic curve E

Description

If the curve has equation y^2 +/- f, then the bundle is represented by a vector bundle on PP^1 and a matrix representing the action of y. the only key is yAction

i1 : kk = ZZ/101

o1 = kk

o1 : QuotientRing
 
i2 : R = kk[s,t]

o2 = R

o2 : PolynomialRing
 
i3 : f = (s+2*t)*(s+t)*(s-t)*(s-2*t)

      4     2 2     4
o3 = s  - 5s t  + 4t

o3 : R
 
i4 : L0 = randomLineBundle(0,f)

o4 = VectorBundleOnE{...1...}

o4 : VectorBundleOnE
 
i5 : (degOnE L0, orderInPic L0)

o5 = (0, 60)

o5 : Sequence

See also

Methods that use an object of class VectorBundleOnE:

  • degOnE(VectorBundleOnE) -- see degOnE -- degree of a vector bundle on E
  • orderInPic(VectorBundleOnE) -- see orderInPic -- order of a line bundle of degree 0 in Pic(E)
  • randomExtension(VectorBundleOnE,VectorBundleOnE) -- see randomExtension -- a random extension of a vector bundle on E by another vector bundle
  • tensorProduct(CliffordModule,VectorBundleOnE) -- see tensorProduct -- tensor product of sheaves on the elliptic curve or sheaf times CliffordModule
  • tensorProduct(VectorBundleOnE,VectorBundleOnE) -- see tensorProduct -- tensor product of sheaves on the elliptic curve or sheaf times CliffordModule
  • translateIsotropicSubspace(CliffordModule,VectorBundleOnE,PolynomialRing) -- see translateIsotropicSubspace -- choose a random isotropic subspace

For the programmer

The object VectorBundleOnE is a type, with ancestor classes MutableHashTable < HashTable < Thing.

The source of this document is in /build/reproducible-path/macaulay2-1.26.06+ds/M2/Macaulay2/packages/PencilsOfQuadrics.m2:2667:0.