On the singular sheaves in the fine Simpson moduli spaces of 1-dimensional sheaves supported on plane quartics
Oleksandr Iena
TL;DR
This paper investigates the structure of certain moduli spaces of 1-dimensional sheaves on plane quartics, revealing that the non-locally free sheaves form a connected, singular subvariety of codimension 2.
Contribution
It characterizes the subvariety of non-locally free sheaves within the Simpson moduli space, showing its connectedness and singularity properties.
Findings
The subvariety of non-locally free sheaves is connected.
This subvariety is singular.
It has codimension 2 in the moduli space.
Abstract
In the case of the fine Simpson moduli spaces of 1-dimensional sheaves supported on plane quartics, the subvariety of sheaves that are not locally free on their support is connected, singular, and has codimension 2.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Algebraic structures and combinatorial models