Next: Sheaves
Up: Algebraic Geometry
Previous: Algebraic Geometry
Schemes
New Features:
- Tests have been added for whether an ordinary projective scheme
is Gorenstein, Cohen-Macaulay or the arithmetic versions of these:
IsGorenstein, IsArithmeticallyGorenstein and the same
with Gorenstein replaced by CohenMacaulay.
- A package of code to work with divisors on varieties has been added.
This is in an early stage of development but contains a range of
intrinsics to create divisors, decompose into primary or prime
components, work with Q-rational divisors, perform basic
arithmetic, compute Riemann-Roch spaces, test for linear
equivalence, compute intersection numbers for divisors on
surfaces and give a representative divisor for an invertible
sheaf, which includes computing canonical divisors. The
functionality in parts relies on sheaf operations or
slight adaptations and so requires the base scheme to be
ordinary projective.
- An intrinsic has been added to test whether an isolated
singularity on a scheme is analytically isomorphic
to a hypersurface singularity, IsHypersurfaceSingularity.
In the affirmative case this will also return the
analytically equivalent hypersurface equation expanded
to desired precision and give the transformation from
the original coordinates. The user can further
expand the analytic hypersurface equation at a later stage
with HypersurfaceSingularityExpandFurther and also
expand a rational function in the local analytic
coordinates with HypersurfaceSingularityExpandFunction.
Next: Sheaves
Up: Algebraic Geometry
Previous: Algebraic Geometry