K3 surfaces

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This returns a list of polarised K3 surfaces X,A embedded in weighted projective space X⊂P(w₀,...,w_N) by all multiples of A that match the given data.

Weights	w₀,...,w_N	e.g. 1,3,7
Codimension	N−2
Genus	h⁰(X,A)−1
Hilbert series	P_X,A(t)	1 + t + t² + t³ + t⁴ + t⁵ + t⁶ + ...
Basket	B	e.g. [2,1],2x[5,2]
Basket size	#B
Singular rank	Σ r_i−1
Degree	A²	e.g. 1/6 or 0.35
Projections	Type	I II₁ II₂ II₃ II₄ II₅ II₆ II₇ IV
Unprojections	Type	I II₁ II₂ II₃ II₄ II₅ II₆ II₇ IV

Authors and references

This data is provided by Selma Altinok, Gavin Brown, Anthony Iano-Fletcher, and Miles Reid.

Further details can be found in:

G Brown, "A database of polarized K3 surfaces", Experiment. Math. 16 (1), 2007, 7-20^[BibTeX/MR]
S Altinok, G Brown, M Reid, "Fano 3-folds, K3 surfaces and graded rings", Topology and geometry: commemorating SISTAG, Contemp. Math., 314 (2002), 25-53^[BibTeX/MR]

Please consider citing the above references if you use this data.

K3 surfaces

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