HDI(phi, i, D)
phi_*^i D
This method implements Algorithm A.8 in "Reduced \v{C}ech complexes and computing higher direct images under toric maps".
The first Hirzebruch surface $\mathbb{F}_1$ has two geometric interpretations: 1) as the projective bundle $\mathbb{P}(\mathcal{O}_{\mathbb{P}^1} \oplus \mathcal{O}_{\mathbb{P}^1})$ or as the blowup of $\mathbb{P}^2$ at a torus-fixed point. In both cases we get a toric morphism, the projection and blowdown map. In the first case, the (higher) direct images of a line bundle are themselves vector bundles, and hence split.
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In the second case, we can find line bundles whose (higher) direct images which have relations or torsion.
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The object HDI is a method function.
The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/ToricHigherDirectImages.m2:930:0.