Abstract

) to the reader.4.3. The minimality of the canonical toric resolutions. We study when the canonicaltoric resolution of a weighted homogeneous surface is minimal. Though the canonical toricresolution is not always minimal (see Example 28), we can expect that the minimality hold foralmost all classes of non-degenerate surfaces. By [9, III(6.3)], for each weighted homogeneoussurface the resolution graph associated with the canonical toric resolution is star-shaped.Hence, when the resolution graph has at least three arms, the canonical resolution is minimal.We have the following general statement which is very helpful to see if a given toric modi-fication is minimal.Lemma 21.

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