Abstract
We use the computer algebra system Magma to study graded rings of Fano 3-folds of index ≥ 3 in terms of their Hilbert series.
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References
S. Altinok, G. Brown and M. Reid, Fano 3-folds,K3 surfaces and graded rings. Topology and geometry: commemorating SISTAG, Contemp. Math.,314 (2002), 25–53.
G. Brown, A database of polarised K3 surfaces. Exp. Math., 2006, to appear.
G. Brown and K. Suzuki, Lists of examples and Magma code available for download at www.kent.ac.uk/ims/grdb.
A.R. Iano-Fletcher, Working with weighted complete intersections. Explicit birational geometry of 3-folds (A. Corti and M. Reid eds.), LMS Lecture Note Ser.,281, CUP, 2000, 101–173.
V.A. Iskovskikh and Yu.G. Prokhorov, Fano Varieties. Algebraic geometry V, Encyclopaedia of Mathematical Sciences,47, Springer-Verlag, Berlin, 1999.
Y. Kawamata, Boundedness of ℚ-Fano Threefolds. Contemp. Math.,131 (1992), 439–445.
W. Bosma, J. Cannon and C. Playoust, The Magma algebra system I: The user language. J. Symb. Comp.,24 (1997), 235–265.
M. Reid, Young person’s guide to canonical singularities. Algebraic Geometry (Bowdoin 1985), vol. 1, S. Bloch ed., Proc. of Symposia in Pure Math.,46, AMS, 1987, 345–414.
M. Reid, Graded rings and birational geometry, Proc. of algebraic geometry symposium (Kinosaki, Oct 2000), K. Ohno (ed.), 1–72.
K. Suzuki, On ℚ-Fano 3-folds with Fano index ≥ 9. Manuscripta Mathematica,114, Springer, 229–246.
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Brown, G., Suzuki, K. Computing certain Fano 3-folds. Japan J. Indust. Appl. Math. 24, 241 (2007). https://doi.org/10.1007/BF03167538
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DOI: https://doi.org/10.1007/BF03167538