The A-infinity Algebra of a Curve and the J-invariant
| dc.contributor.advisor | Polishchuk, Alexander | en_US |
| dc.contributor.author | Fisette, Robert | en_US |
| dc.creator | Fisette, Robert | en_US |
| dc.date.accessioned | 2012-10-26T03:58:22Z | |
| dc.date.available | 2012-10-26T03:58:22Z | |
| dc.date.issued | 2012 | |
| dc.description.abstract | We choose a generator G of the derived category of coherent sheaves on a smooth curve X of genus g which corresponds to a choice of g distinguished points P1, . . . , Pg on X. We compute the Hochschild cohomology of the algebra B = Ext (G,G) in certain internal degrees relevant to extending the associative algebra structure on B to an A1-structure, which demonstrates that A1-structures on B are finitely determined for curves of arbitrary genus. When the curve is taken over C and g = 1, we amend an explicit A1-structure on B computed by Polishchuk so that the higher products m6 and m8 become Hochschild cocycles. We use the cohomology classes of m6 and m8 to recover the j-invariant of the curve. When g 2, we use Massey products in Db(X) to show that in the A1-structure on B, m3 is homotopic to 0 if and only if X is hyperelliptic and P1, . . . , Pg are chosen to be Weierstrass points. iv | en_US |
| dc.identifier.uri | https://hdl.handle.net/1794/12368 | |
| dc.language.iso | en_US | en_US |
| dc.publisher | University of Oregon | en_US |
| dc.rights | All Rights Reserved. | en_US |
| dc.subject | A-infinity | en_US |
| dc.subject | Curve | en_US |
| dc.subject | Elliptic curve | en_US |
| dc.subject | Hochschild cohomology | en_US |
| dc.subject | j-invariant | en_US |
| dc.title | The A-infinity Algebra of a Curve and the J-invariant | en_US |
| dc.type | Electronic Thesis or Dissertation | en_US |
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