Next: Arithmetic Geometry
Up: Algebraic Geometry
Previous: Algebraic Curves [HB 93]
Hilbert Series of Polarised Varieties [HB 95]
New Features:
- The K3 database now contains 24,099 objects (an increase from
around 400 in previous versions). In a precise sense, this
now represents all possible (infinitely many) Hilbert series
that may be associated to a polarised K3 surface.
- The machinery used to generate the database has been lifted
to the user level. This includes new datatypes for
(the numerical data associated to) polarised singularities
and polarised varieties.
- There is a small database of Fano 3-folds. A major point of
this work has been to contribute to the (hopefully imminent)
classification of Fano 3-folds. This small database is
the first step of what may become the comprehensive classification
of (Hilbert series of) Fano 3-folds.
- New Riemann-Roch formulas used to compute Hilbert series have
been included. This allows one to make
graded ring calculations for K3 surfaces, Fano 3-folds, Calabi-Yau
3-folds and curves polarised by a subcanonical divisor.
It is possible for a user to generate many families of these
varieties interactively--a typical application of these methods
is to generate large numbers of examples.
- A facility for users to write and read their own graded ring
databases has been added. This makes genuine binary data files
together with various indexing methods, as is usual with Magma
databases, and it is essential when one generates large numbers
of examples.
Next: Arithmetic Geometry
Up: Algebraic Geometry
Previous: Algebraic Curves [HB 93]