ar X iv : 0 90 5 . 21 69 v 1 [ m at h . A G ] 1 3 M ay 2 00 9 Enriques diagrams , infinitely near points , and Hilbert schemes
نویسنده
چکیده
We study sequences of infinitely near T -points of a smooth family F/Y of geometrically irreducible surfaces. We destinguish a special sort of such sequences, the strict sequences. To each one, we associate an ordered unweighted Enriques diagram. We prove that the various sequences with a given diagram form a functor, and we represent it by a smooth Y -scheme. We equip this scheme with a free action of the automorphism group of the diagram. We equip the diagram with weights, take the subgroup of automorphisms preserving the weights, and form the corresponding quotient scheme. Our main theorem asserts the existence of a universally injective map from this quotient scheme to the Hilbert scheme of F/Y ; further, this map is an embedding in characteristic 0. However, in every positive characteristic, we give an example where the map is purely inseparable.
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