cubic-4-folds's Issues
Number of Fourier--Mukai partners
Description of the surface
See https://math.dartmouth.edu/~auel/papers/docs/slc2015_handout.pdf, but surely there is another reference with more details?
Make a similar table for other Fano 4-folds
There is a similar theory for other Fano 4-folds. @8d1h made the following suggestion:
The same table for EPW/GM 4-folds (following for example "Special prime Fano fourfolds of degree 10 and index 2" https://doi.org/10.1017/CBO9781107416000.009), although I do agree that more people are interested in the cubic 4-fold case.
Some ideas to improve things
- have
(**')
before(**)
, so order by containment and not date - think of a way to make the degree of the (twisted) K3 better, like
2 (3)
and writedegree of K3 surface (order of Brauer class)
, or maybe write2\cdot 7^2
- give information about the special surfaces it contains: could be a nice description with some numerical data, or just the existence together with a reference
In http://content.algebraicgeometry.nl/2017-3/2017-3-015.pdf the special surface is always the blowup of the projective plane in a certain number of points. Just give that as the description.
Numerical invariants for special surfaces: if S
is the surface, then
S^2
: self-intersectionh^2S
: degree
In Nuer's paper: H
is the restriction of O(1)
to the blowup of the projective plane.
Hassett calls degree <h^2,T>
, which in Nuer is H^2
. To compute the self-intersection from the degree, the discriminant d
is 3T^2-(h^2.T)^2
.
Number of Fourier--Mukai partners
Automorphism groups of cubic 4-folds
Is https://arxiv.org/abs/2308.07186v1 interesting / feasible to include?
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