Euler characteristics of Hilbert schemes of points on simple surface singularities
We study the geometry and topology of Hilbert schemes of points on the orbifold surface [C2/G], respectively the singular quotient surface C2/G, where G < SL(2, C) is a finite subgroup of type A or D. We give a decomposition of the (equivariant) Hilbert scheme of the orbifold into affine spac...
| Հիմնական հեղինակներ: | , , |
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| Ձևաչափ: | Journal article |
| Հրապարակվել է: |
Springer International Publishing
2018
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| Ամփոփում: | We study the geometry and topology of Hilbert schemes of points on the orbifold surface [C2/G], respectively the singular quotient surface C2/G, where G < SL(2, C) is a finite subgroup of type A or D. We give a decomposition of the (equivariant) Hilbert scheme of the orbifold into affine space strata indexed by a certain combinatorial set, the set of Young walls. The generating series of Euler characteristics of Hilbert schemes of points of the singular surface of type A or D is computed in terms of an explicit formula involving a specialized character of the basic representation of the corresponding affine Lie algebra; we conjecture that the same result holds also in type E. Our results are consistent with known results in type A, and are new for type D. |
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