Crepant resolution

In algebraic geometry, a crepant resolution of a singularity is a resolution that does not affect the canonical class of the manifold. The term "crepant" was coined by Miles Reid (1983) by removing the prefix "dis" from the word "discrepant", to indicate that the resolutions have no discrepancy in the canonical class.

The crepant resolution conjecture of Ruan (2006) states that the orbifold cohomology of a Gorenstein orbifold is isomorphic to a semiclassical limit of the quantum cohomology of a crepant resolution.

In 2 dimensions, crepant resolutions always exist and are unique, in 3 dimensions they exist but need not be unique as they can be related by flops, and in dimensions greater than 3 they need not exist.

References

• Reid, Miles (1983), "Minimal models of canonical 3-folds", Algebraic varieties and analytic varieties, proceedings of the Angiers 'Journees de Geometrie Algebrique' (1979) (Tokyo, 1981), Adv. Stud. Pure Math., 1, Amsterdam: North-Holland, pp. 131–180, MR715649 
• Ruan, Yongbin (2006), "The cohomology ring of crepant resolutions of orbifolds", Gromov-Witten theory of spin curves and orbifolds, Contemp. Math., 403, Providence, R.I.: American Mathematical Society, pp. 117–126, MR2234886