Enriques图、任意近点和Hilbert格式
Enriques diagrams, arbitrarily near points, and Hilbert schemes
摘要：
给定一个光滑的几何不可约曲面族F/Y，研究了F/Y的任意近T点序列，推广了传统的单个光滑曲面的无穷近点序列.我们区分这些新序列的一种特殊类型，严格序列。对于每个严格序列，我们关联一个有序的未加权Enriques图。我们证明了具有固定图的各种序列形成一个函子，并将其表示为光滑的Y-概型。我们装备这个Y-计划与自由行动的自同构群的图。我们给图赋予权，取那些保持权的自同构的子群，并形成相应的商方案。我们的主要定理构造了一个从这个商方案到F/Y的Hilbert方案的正则泛内射映射，进一步地，这个映射是特征0中的嵌入。然而，在每一个正的特征中，我们在附录B中给出了一个例子，其中地图是完全不可分的。
英文摘要：
Given a smooth family F/Y of geometrically irreducible surfaces, we study sequences of arbitrarily near T-points of F/Y; they generalize the traditional sequences of infinitely near points of a single smooth surface. We distinguish a special sort of these new sequences, the strict sequences. To each strict sequence, we associate an ordered unweighted Enriques diagram. We prove that the various sequences with a fixed diagram form a functor, and we represent it by a smooth Y-scheme. We equip this Y-scheme with a free action of the automorphism group of the diagram. We equip the diagram with weights, take the subgroup of those automorphisms preserving the weights, and form the corresponding quotient scheme. Our main theorem constructs a canonical universally injective map Ψfrom 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, in Appendix B, where the map is purely inseparable.
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