K3 surfaces (original) (raw)
General search
This returns a list of polarised K3 surfaces X,A embedded in weighted projective space X⊂P(w0,...,wN) by all multiples of A that match the given data.
| Weights | w0,...,wN | e.g. 1,3,7 | |
|---|---|---|---|
| Codimension | N−2 | ||
| Genus | h0(X,A)−1 | ||
| Hilbert series | PX,A(t) | 1 + t + t2 + t3 + t4 + t5 + t6 + ... | |
| Basket | B | e.g. [2,1],2x[5,2] | |
| Basket size | #B | ||
| Singular rank | Σ ri−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.