Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on resolution of rational and hypersurface singularities   It is well known that the exceptional set in a resolution of a rational
surface singularity is a tree of rational curves. We generalize the
combinatoric part of this statement to higher dimensions and show that the
highest cohomologies of the dual complex associated to a resolution of an
isolated rational singularity vanish. We also prove that the dual complex
associated to a resolution of an isolated hypersurface singularity is simply
connected. As a consequence, we show that the dual complex associated to a
resolution of a 3-dimensional Gorenstein terminal singularity has the homotopy
type of a point.

29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs