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In algebraic geometry, general elephant is an idiosyncratic name for a general element of the anticanonical system of a variety, introduced by Miles Reid.[1] For 3-folds the general elephant problem (or conjecture) asks whether general elephants have at most du Val singularities; this has been proved in several cases.[2][3]

References

  1. ^ Reid, M. (1985). Young person's guide to canonical singularities. Proceedings of Symposia in Pure Mathematics. Vol. 46. pp. 345–414. doi:10.1090/pspum/046.1/927963. ISBN 9780821814765. S2CID 116194977.
  2. ^ Kawakita, Masayuki (2003). "General Elephants of Three-Fold Divisorial Contractions". Journal of the American Mathematical Society. 16 (2): 331–362. doi:10.1090/S0894-0347-02-00416-2. ISSN 0894-0347. JSTOR 30041435.
  3. ^ Prokhorov, Yuri (1996). "On the general elephant conjecture for Mori conic bundles". arXiv:alg-geom/9608007.


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