Dual graphs of exceptional divisors

Publication date: 12 March 2012

Abstract: 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.

Mathematics Subject Classification ID

Determinantal varieties (14M12) Singularities of surfaces or higher-dimensional varieties (14J17) Homotopy theory and fundamental groups in algebraic geometry (14F35)

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