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- W4360610413 abstract "A primitive multiple scheme is a Cohen-Macaulay scheme $Y$ such that the associated reduced scheme $X=Y_{red}$ is smooth, irreducible, and that $Y$ can be locally embedded in a smooth variety of dimension $dim(X)+1$. If $n$ is the multiplicity of $Y$, there is a canonical filtration $X=X_1subset X_2subsetcdotssubset X_n=Y$, such that $X_i$ is a primitive multiple scheme of multiplicity $i$. The simplest example is the trivial primitive multiple scheme of multiplicity $n$ associated to a line bundle $L$ on $X$: it is the $n$-th infinitesimal neighborhood of $X$, embedded in the line bundle $L^*$ by the zero section. The main subject of this paper is the construction and properties of fine moduli spaces of vector bundles on primitive multiple schemes. Suppose that $Y=X_n$ is of multiplicity $n$, and can be extended to $X_{n+1}$ of multiplicity $n+1$, and let $M_n$ a fine moduli space of vector bundles on $X_n$. With suitable hypotheses, we construct a fine moduli space $M_{n+1}$ for the vector bundles on $X_{n+1}$ whose restriction to $X_n$ belongs to $M_n$. It is an affine bundle over the subvariety $N_nsubset M_n$ of bundles that can be extended to $X_{n+1}$. In general this affine bundle is not banal. This applies in particular to Picard groups. We give also many new examples of primitive multiple schemes $Y$ such that the dualizing sheaf $omega_Y$ is trivial." @default.
- W4360610413 created "2023-03-24" @default.
- W4360610413 creator A5069639820 @default.
- W4360610413 date "2023-05-17" @default.
- W4360610413 modified "2023-09-24" @default.
- W4360610413 title "Moduli of vector bundles on primitive multiple schemes" @default.
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- W4360610413 doi "https://doi.org/10.1142/s0129167x23500350" @default.
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