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Algebraic Surfaces
New Features:
- For a curve C defined over a global field F (the rationals,
a number field or a univariate function field), and a prime p
of the ring of integers
ZF, one may obtain a RegularModel
of the associated arithmetic surface. The model has generic fibre
C, and is regular on its special fibre above p; however it is
not necessarily a minimal model.
The routine returns an object of type CrvRegModel which
stores a number of patches that define the model, as well as
the components of the special fibre and other data.
From this object, one may access information of interest such as
the ComponentGroup of the Jacobian. One may also access
equations for the patches of the model, and
The current implementation imposes some extra restrictions on which
curves and fields are allowed; this will improve in subsequent releases.
Also, additional functions to extract information from regular models
may be added on request.
- The new intrinsic ParametrizeDegree5DelPezzo is provided for
parametrizing a degree 5 Del Pezzo surface (that may be singular,
i.e., degenerate) anti-canonically embedded in P5. This is also
linked to the general rational hypersurface parametrization routine
ParametrizeProjectiveHypersurface, plugging that special case gap.
The parametrization routines for degree 7 and 8 Del Pezzos have been updated
for speed and efficiency and similarly for the parametrization of Rational
Scrolls.
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Previous: Sheaves
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