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deltaE -- the polytope of possible degrees that give non zero cohomology

Description

For a toric vector bundle over a complete toric variety there is a finite set of degrees $u$ such that the degree $u$ part of the cohomology of the vector bundle is non-zero. This function computes a polytope $\Delta_E$, such that these degrees are contained in this polytope. If the underlying toric variety is not complete then an error is returned.
i1 : E = toricVectorBundle(2,pp1ProductFan 2)

o1 = {dimension of the variety => 2 }
      number of affine charts => 4
      number of rays => 4
      rank of the vector bundle => 2

o1 : ToricVectorBundleKlyachko
i2 : P = deltaE E

o2 = P

o2 : Polyhedron
i3 : vertices P

o3 = 0

              2       1
o3 : Matrix QQ  <-- QQ
i4 : E1 = tangentBundle projectiveSpaceFan 2

o4 = {dimension of the variety => 2 }
      number of affine charts => 3
      number of rays => 3
      rank of the vector bundle => 2

o4 : ToricVectorBundleKlyachko
i5 : P1 = deltaE E1

o5 = P1

o5 : Polyhedron
i6 : vertices P1

o6 = | -1 2  -1 |
     | -1 -1 2  |

              2       3
o6 : Matrix QQ  <-- QQ

See also

Ways to use deltaE:

  • deltaE(ToricVectorBundle)

For the programmer

The object deltaE is a method function.


The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/ToricVectorBundles.m2:2745:0.