Fano 3-folds

General search

This returns a list of Fano 3-folds X⊂P(w0,...,wN) that match the given data. The degree 1 hyperplane A that polarises X satisfies -KX = fA where f is the Fano index of X.

w0,...,wN
S∈|-KX|
N−3
f
h0(X,-KX)−2
PX(t)
1 + t + t2 + t3 + t4 + t5 + t6 + t7 + t8 + ...
B
e.g. 3x1/5(1,2,3)
#B
A3
Σr - 1
Σr - (1/r)
(K2-3c2)A
e.g. ≤ 0 to prevent Ω1** being necessarily unstable
Type
I   II1   II2   II3   II4   II5   II6   II7   IV
Type
I   II1   II2   II3   II4   II5   II6   II7   IV

Find by database ID

e.g. 1 or 1,2,3,4

Authors and references

This data is provided by Selma Altinok, Gavin Brown, Anthony Iano-Fletcher, Miles Reid, and Kaori Suzuki. Warning: the lists of Fanos of index > 2 are under construction. They are classifications of basket-genus pairs, and will be refined following results of Prokhorov and Reid.

Further details can be found in:

Please cite one of the above references if you use this data.