General elephant

{{confusing|date=October 2022}}

In algebraic geometry, general elephant is an idiosyncratic name for a general element of the anticanonical system of a variety, introduced by Miles Reid.{{Cite book |last=Reid |first=M. |date=1985 |title=Young person's guide to canonical singularities |series=Proceedings of Symposia in Pure Mathematics |volume=46 |issue=1 |pages=345–414 |doi=10.1090/pspum/046.1/927963 |isbn=9780821814765 |s2cid=116194977 |language=en}} 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.{{Cite journal |last=Kawakita |first=Masayuki |date=2003 |title=General Elephants of Three-Fold Divisorial Contractions |journal=Journal of the American Mathematical Society |volume=16 |issue=2 |pages=331–362 |doi=10.1090/S0894-0347-02-00416-2 |jstor=30041435 |issn=0894-0347|doi-access=free }}{{Cite arXiv |last=Prokhorov |first=Yuri |date=1996 |title=On the general elephant conjecture for Mori conic bundles |eprint=alg-geom/9608007}}