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Toric Varieties
New Features:
- Algorithms have been implemented for computing the Demazure roots of the
complete fan F
. The intrinsic DemazureRoots(F) returns the roots
partitioned into two sets: the semistable roots and the unipotent roots.
The number of Demazure roots can be found via NumberOfRoots(F).
- The new intrinsic IsSemistable(F) can be used to determine whether
the complete fan F
is semistable. Similarly, IsReductive(X) returns
true if and only if the projective variety X
has reductive automorphism group.
- The intrinsics IsIsomorphicToProjectiveSpace(X) and
IsIsomorphicToProductProjectiveSpace(X) use the Demazure roots of
the associated fan to determine whether the complete toric variety X
is
isomorphic to a (product of) projective space.
Changes:
- The intrinsics IsPrincipal(D) and IsLinearlyEquivalent(D,E)
for toric divisors D
and E
now also return a rational function f
such that D = div(f )
or
D = E + div(f )
, respectively.
- A significant speed improvement and reduction in the memory footprint of
CartierToWeilMap(X) has been made. This intrinsic is fundamental
when working with toric divisors, and returns the embedding map from the
lattice of torus-invariant Cartier divisors to the lattice of torus-invariant
Weil divisors.
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