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We describe Milnor open books and Legendrian surgery diagrams for canonicalcontact structures of links of some rational surface singularities. We alsodescribe an infinite family of Milnor fillable contact 3-manifolds so that theMilnor genus (resp. Milnor norm) is strictly greater than the support genus(resp. support norm) of the canonical contact structure, for each member ofthis family.

Milnor open books of links of some rational surface singularities