McKay Correspondence over Non Algebraically Closed Fields

@article{Blume2014McKayCO,
  title={McKay Correspondence over Non Algebraically Closed Fields},
  author={Mark Blume},
  journal={arXiv: Algebraic Geometry},
  year={2014},
  pages={47-75}
}
  • Mark Blume
  • Published 23 January 2006
  • Mathematics
  • arXiv: Algebraic Geometry
The classical McKay correspondence for finite subgroups G of \(\mathrm{SL}(2, \mathbb{C})\) gives a bijection between isomorphism classes of nontrivial irreducible representations of G and irreducible components of the exceptional divisor in the minimal resolution of the quotient singularity \(\mathbb{A}_{\mathbb{C}}^{2}/G\). Over non algebraically closed fields K there may exist representations irreducible over K which split over \(\overline{K}\). The same is true for irreducible components of… 

References

SHOWING 1-10 OF 27 REFERENCES

McKay Correspondence and Hilbert Schemes

Introduction. A particular case in the superstring theory where a finite group G acts upon the target Calabi-Yau manifold M in the theory seems to attract both physicists' and mathematician's

Hilbert schemes and simple singularities

The first half of this article is expository; it contains a brief survey of the famous ADE classification, and how it applies to six kinds of objects, some old and some relatively new. The second

Construction of G‐Hilbert schemes

In this paper we construct G‐Hilbert schemes for finite group schemes G. We find a construction of G‐Hilbert schemes as relative G‐Hilbert schemes over the quotient that does not need the Hilbert

Construction géométrique de la correspondance de McKay

© Gauthier-Villars (Éditions scientifiques et médicales Elsevier), 1983, tous droits réservés. L’accès aux archives de la revue « Annales scientifiques de l’É.N.S. » (http://www.

Rational singularities, with applications to algebraic surfaces and unique factorization

© Publications mathématiques de l’I.H.É.S., 1969, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://

Hilbert schemes of abelian group orbits.

For G a finite abelian subgroup of SL(3, k) we construct a crepant resolution of the quotient variety A/G in a canonical way.

A Course in Arithmetic

Part 1 Algebraic methods: finite fields p-adic fields Hilbert symbol quadratic forms over Qp, and over Q integral quadratic forms with discriminant +-1. Part 2 Analytic methods: the theorem on