Wild quotient singularities of surfaces

作者：Lorenzini Dino^*

来源：Mathematische Zeitschrift, 2013, 275(1-2): 211-232.

DOI：10.1007/s00209-012-1132-7

• Cyclic quotient singularity
• Wild
• Intersection matrix
• Resolution graph
• Fundamental cycle

Let be a noetherian regular local ring of dimension with residue field of characteristic . Assume that is endowed with an action of a finite cyclic group whose order is divisible by . Associated with a resolution of singularities of is a resolution graph and an intersection matrix . We prove in this article three structural properties of wild quotient singularities, which suggest that in general, one should expect when that the graph is a tree, that the Smith group is killed by , and that the fundamental cycle has self-intersection . We undertake a combinatorial study of intersection matrices with a view towards the explicit determination of the invariants and . We also exhibit explicitly the resolution graphs of an infinite set of wild -singularities, using some results on elliptic curves with potentially good ordinary reduction which could be of independent interest.

• 出版日期2013-10