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 sheave...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.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.21022107 and 11771229)。
文摘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.
