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A-infinity structures associated with curves (NAGRT) March 25, 2013 (10:00 AM PDT - 11:00 AM PDT)
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Location: MSRI: Simons Auditorium
Speaker(s) Alexander Polishchuk (University of Oregon)
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The talk is based on my joint work with Robert Fisette.
We consider the A-infinity algebra associated with a certain generator of the derived category of coherent sheaves on a smooth projective curve. In the case of an elliptic curve this A-infinity algebra can be computed explicitly, and in particular, one can recover the j-invariant by looking at the higher products m_6 and m_8. In the higher genus curve we prove that the A-infinity structure can be uniquely recovered up to homotopy from the higher products up to m_6. We also study the map from the moduli space of curves with marked points given by the products m_3.

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