General elephant

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.²³

References

Reid, Miles (1987), "Young person's guide to canonical singularities", Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985), Proc. Sympos. Pure Math., vol. 46, Providence, R.I.: American Mathematical Society, pp. 345–414, MR 0927963

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.
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. hdl:2433/214762. ISSN 0894-0347. JSTOR 30041435.
Prokhorov, Yuri (1996). "On the general elephant conjecture for Mori conic bundles". arXiv:alg-geom/9608007.

[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. hdl:2433/214762. ISSN 0894-0347. JSTOR 30041435.

[3] Prokhorov, Yuri (1996). "On the general elephant conjecture for Mori conic bundles". arXiv:alg-geom/9608007.

1

2

3