index.rst

Documentation for the Hodge diamond cutter

.. toctree::
    :maxdepth: 2
    :caption: Contents

.. automodule:: diamond.diamond

Hodge diamonds

.. autoclass:: diamond.HodgeDiamond
    :members:
    :special-members:
    :member-order: bysource

Hochschild homology

.. autoclass:: diamond.HochschildHomology
    :members:
    :member-order: bysource

Constructions

Elementary constructions

.. autofunction:: diamond.zero

.. autofunction:: diamond.point

.. autofunction:: diamond.lefschetz

.. autofunction:: diamond.Pn

.. autofunction:: diamond.hypersurface

.. autofunction:: diamond.weighted_hypersurface

.. autofunction:: diamond.cyclic_cover

.. autofunction:: diamond.complete_intersection

Curves and moduli spaces of sheaves on them

.. autofunction:: diamond.curve

.. autofunction:: diamond.symmetric_power

.. autofunction:: diamond.jacobian

.. autofunction:: diamond.moduli_vector_bundles

.. autofunction:: diamond.seshadris_desingularisation

.. autofunction:: diamond.moduli_parabolic_vector_bundles_rank_two

.. autofunction:: diamond.quot_scheme_curve

Surfaces and moduli spaces of sheaves on them

.. autofunction:: diamond.surface

.. autofunction:: diamond.ruled

.. autofunction:: diamond.K3

.. autofunction:: diamond.enriques

.. autofunction:: diamond.hilbn

.. autofunction:: diamond.nestedhilbn

Abelian varieties and related objects

.. autofunction:: diamond.abelian

.. autofunction:: diamond.kummer_resolution

Fano varieties

These are Hodge diamonds of Fano varieties in the sense that their anticanonical bundle is ample.

The term "Fano variety" can also mean a variety parametrising linear subspaces on another variety. Some of these are Fano in the first sense, others are not (always). See e.g. :func:`diamond.fano_variety_lines_cubic`.

.. autofunction:: diamond.fano_threefold

.. autofunction:: diamond.gushel_mukai

.. autofunction:: diamond.fano_variety_intersection_quadrics_even

.. autofunction:: diamond.fano_variety_intersection_quadrics_odd

.. autofunction:: diamond.fano_variety_lines_cubic

Homogeneous varieties and closely related constructions

These are also all Fano varieties, but they are grouped together because of their similar origin.

.. autofunction:: diamond.partial_flag_variety

.. autofunction:: diamond.generalised_grassmannian

.. autofunction:: diamond.grassmannian

.. autofunction:: diamond.orthogonal_grassmannian

.. autofunction:: diamond.symplectic_grassmannian

.. autofunction:: diamond.lagrangian_grassmannian

.. autofunction:: diamond.horospherical

.. autofunction:: diamond.odd_symplectic_grassmannian

Moduli spaces attached to quivers

.. autofunction:: diamond.quiver_moduli

Hyperkähler varieties

.. autofunction:: diamond.K3n

.. autofunction:: diamond.generalised_kummer

.. autofunction:: diamond.ogrady6

.. autofunction:: diamond.ogrady10

Other

.. autofunction:: diamond.Mzeronbar