Wild quotients of products of curves
Wild quotients of products of curves
复制标题
曲线乘积的野商
DOI：
10.1007/s40879-017-0174-0
复制
发表时间：
2018
影响因子：
0.6
通讯作者：
Dino J. Lorenzini
中科院分区：
文献类型：
--
作者：
Dino J. Lorenzini
设k是特征p> 0的代数闭域.设和是两条光滑的真连通曲线，每一条曲线都有一个p阶自同构σ i：B i → B i σ i：B i→ B i.设和σ：Y→ Y为自同构.当B_2 B 2是正亏格的普通曲线时，证明了图的任一奇点的分解图是具有三个终端链的星形图.当B_1 B 1也是平凡的，或当σ _1 σ 1有唯一不动点时，分解的交矩阵N满足，并且可以完全确定.奇点是理性的。期望曲面的野商奇点具有作为树的分解图，其关联的交矩阵N对于某些r\geqslane 0 r <$0满足。证明了对任意s> 0 s> 0与p互质，存在有一个结点的分解图，s+ 2 s+ 2终端链，且交矩阵N满足.
Let k be an algebraically closed field of characteristic p> 0 p> 0. Let and be two smooth proper connected curves, each endowed with an automorphism σ _i: B_i → B_i σ i: B i→ B i of order p. Let, and let σ: Y → Y σ: Y→ Y be the automorphism. We show that the graph of the resolution of any singularity of is a star-shaped graph with three terminal chains when B_2 B 2 is an ordinary curve of positive genus. The intersection matrix N of the resolution satisfies, and can be completely determined when B_1 B 1 is also ordinary, or when σ _1 σ 1 has a unique fixed point. The singularity is rational. Wild-quotient singularities of surfaces are expected to have resolution graphs which are trees, with associated intersection matrices N satisfying for some r\geqslant 0 r⩾ 0. We show, for any s> 0 s> 0 coprime to p, the existence of resolution graphs with one node, s+ 2 s+ 2 terminal chains, and with intersection matrix N satisfying.