Dual graphs of exceptional divisors

Details Dual graphs of exceptional divisors Dual graphs of exceptional divisors

2012-03-12

arxiv.org/abs/1203.2640v1

Mathematics

Algebraic Geometry

Scientific paper

Let p be a singular point of a variety. Consider a resolution where the preimage of p is a simple normal crossing divisor E. The combinatorial structure of E is described by a cell complex D(E), called the dual graph or dual complex of E. It is known that the homotopy type of D(E) depends only on p, not on the resolution chosen. We prove that this homotopy type can be arbitrary. We also describe which homotopy types can be obtained from rational singularities.

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