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Description: |
Since its introduction, the Fourier-Mukai transform has been a very important tool for the study of the properties of moduli spaces of sheaves and vector bundles. For instance, Atiyah's characterization of vector bundles allowed Tu to give a geometric description of the moduli spaces of semistable sheaves on smooth elliptic curves. Their results can be obtained in a very simple way as an application of the Fourier-Mukai transform on an elliptic curve. In this talk, we will consider the case of some degenerations of elliptic curves. For a cycle E_N of projective lines, we will show that the connected component of the moduli space of semistable sheaves of degree 0 that contains vector bundles of rank r is isomorphic to the r-th symmetric product of the rational curve with one node. If time permits, we will show how some non-trivial Fourier-Mukai transforms of the derived category of this curve allow also to consider other degrees.
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Date: |
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| Start Time: |
14:30 |
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Speaker: |
Ana Cristina López Martín (Univ. Salamanca, Spain)
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Institution: |
--
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| Research Groups: |
-Algebra and Combinatorics
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See more:
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<Main>
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