computeEigencharacters(phi, i, D)
This method is the implementation of Algorithm A.5 in "Reduced \v{C}ech complexes and computing higher direct images under toric maps". More precisely, the higher direct image sheaf inherits a trivial torus action by the kernel torus $T_K :\!= \ker \phi\vert_{T_X}$, and so splits into a direct sum of sheaves indexed by eigencharacters. This method computes these characters, as well as a pair of divisors $(D,E)$ for use in Algorithm A.8 which computes the higher direct image sheaf.
|
|
|
|
|
One might hope that the set of eigencharacters is a convex set, but this is not always the case. For instance, when $X$ is the blowup of $\mathbb{P}^1 \times \mathbb{P}^1$ at the four torus fixed points and phi is the projection to $\mathbb{P}^1$, we can find an example of a line bundle whose eigencharacters are not convex.
|
|
|
|
The object computeEigencharacters is a method function.
The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/ToricHigherDirectImages.m2:874:0.