Sheaves on non-reduced curves in a projective surface  

作　　者：Yao Yuan 

机构地区：[1]Beijing National Center for Applied Mathematics,Academy for Multidisciplinary Studies,Capital Normal University,Beijing 100048,China

出　　处：《Science China Mathematics》2023年第2期237-250,共14页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.21022107 and 11771229)。

摘　　要：Sheaves on non-reduced curves can appear in moduli spaces of 1-dimensional semistable sheaves over a surface and moduli spaces of Higgs bundles as well.We estimate the dimension of the stack M_(X)(nC,χ)of pure sheaves supported at the non-reduced curve nC(n≥2)with C an integral curve on X.We prove that the Hilbert-Chow morphism h_(L,χ):M_(X)^(H)(L,χ)→|L|sending each semistable 1-dimensional sheaf to its support has all its fibers of the same dimension for X Fano or with the trivial canonical line bundle and|L|contains integral curves.

关 键 词：1-dimensional pure sheaves on projective surfaces Hilbert-Chow morphism Hitchin fibration STACK 

分 类 号：O186.11[理学—数学]