Non-reduced moduli spaces of sheaves on multiple curves
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Jean-Marc Drézet
Abstract
Some coherent sheaves on projective varieties have a non-reduced versal deformation space; for example, this is the case for most unstable rank 2 vector bundles on ℙ2, see [18]. In particular, some moduli spaces of stable sheaves are non-reduced. We consider some sheaves on ribbons (double structures on smooth projective curves): let E be a quasi locally free sheaf of rigid type and let 𝓔 be a flat family of sheaves containing E. We find that 𝓔 is a reduced deformation of E when some canonical family associated to 𝓔 is also flat. We consider also a deformation of the ribbon to reduced projective curves with two components, and find that E can be deformed in two distinct ways to sheaves on the reduced curves. In particular some components M of the moduli spaces of stable sheaves deform to two components of the moduli spaces of sheaves on the reduced curves, and M appears as the “limit” of varieties with two components, whence the non-reduced structure of M.
Communicated by: I. Coskun
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Articles in the same Issue
- Frontmatter
- On the order sequence of an embedding of the Ree curve
- 𝔇⊥-parallel normal Jacobi operators for Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka–Webster connection
- A Krasnosel’skii-type theorem for certain orthogonal polytopes starshaped via k-staircase paths
- Higher algebraic structures in Hamiltonian Floer theory
- Additive structures on f-vector sets of polytopes
- The degree of the tangent and secant variety to a projective surface
- Building lattices and zeta functions
- Quaternionic equiangular lines
- Non-reduced moduli spaces of sheaves on multiple curves
Articles in the same Issue
- Frontmatter
- On the order sequence of an embedding of the Ree curve
- 𝔇⊥-parallel normal Jacobi operators for Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka–Webster connection
- A Krasnosel’skii-type theorem for certain orthogonal polytopes starshaped via k-staircase paths
- Higher algebraic structures in Hamiltonian Floer theory
- Additive structures on f-vector sets of polytopes
- The degree of the tangent and secant variety to a projective surface
- Building lattices and zeta functions
- Quaternionic equiangular lines
- Non-reduced moduli spaces of sheaves on multiple curves
