Moduli of vector bundles on primitive multiple schemes
Jean-Marc Dr\'ezet

TL;DR
This paper develops the theory of moduli spaces for vector bundles on primitive multiple schemes, extending existing moduli spaces to higher multiplicities and providing new examples with trivial dualizing sheaves.
Contribution
It constructs fine moduli spaces of vector bundles on primitive multiple schemes and describes their properties, including the extension from multiplicity n to n+1.
Findings
Construction of a fine moduli space $M_{n+1}$ from $M_n$ under certain conditions
Description of the affine bundle structure over subvarieties of the moduli space
New examples of primitive multiple schemes with trivial dualizing sheaf
Abstract
A primitive multiple scheme is a Cohen-Macaulay scheme such that the associated reduced scheme is smooth, irreducible, and that can be locally embedded in a smooth variety of dimension . If is the multiplicity of , there is a canonical filtration , such that is a primitive multiple scheme of multiplicity . The simplest example is the trivial primitive multiple scheme of multiplicity associated to a line bundle on : it is the -th infinitesimal neighborhood of , embedded in the line bundle 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 is of multiplicity , and can be extended to of multiplicity , and let a fine moduli…
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