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Description: |
A primitive multiple curve is a Cohen-Macaulay irreducible projective curve Y that can be locally embedded in a smooth surface, and such that Yred is smooth. These curves have been defined and studied by C. Banica and O. Forster in 1984.
In 1995, D. Bayer and D. Eisenbud gave a complete description of the double curves (called also ribbons). This can be extended to primitive curves of arbitrary multiplicity.
The coherent sheaves on Y are more complicated than on a smooth curve. In particular theycan be non locally free at every point. We will give a description of their structure and some consequences on moduli spaces on semi-stable sheaves on Y.
The deformation of double primitive curves to smooth curves has been studied by M. González in 2006. In general, suppose that we have a flat family of curves π : C → S, where S ⊂ C a neighbourhood of 0, such that π-1(0) = Y and that all the other fibers are smooth irreducible curves. Let OC(1) be a very ample line bundle on C and P a polynomial with rational coefficients. it is not always true that the relative moduli space of semi-stable sheaves MOC(1)(P) → S is flat. I conjecture that this is true if instead of deformations to smooth curves we consider deformations to reduced curves with the maximal number of components (which is the multiplicity of Y ). We give the first results obtained in the theory of such deformations, when the components of the reducible reduced fibers are disjoint (fragmented deformations), or if Y is a double curve.
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Date: |
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| Start Time: |
14:30 |
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Speaker: |
Jean-Marc Drézet (Institut de mathématiques de Jussieu, France)
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Institution: |
Institut de mathématiques de Jussieu (France)
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Place: |
Room 5.5 DMUC
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| Research Groups: |
-Algebra and Combinatorics
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See more:
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<Main>
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