Browsing University Archives by Subject "j-invariant"

Polishchuk, Alexander Fisette, Robert Fisette, Robert 2012-10-26T03:58:22Z 2012-10-26T03:58:22Z 2012 http://hdl.handle.net/1794/12368 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 University of Oregon All Rights Reserved. A-infinity Curve Elliptic curve Hochschild cohomology j-invariant The A-infinity Algebra of a Curve and the J-invariant Electronic Thesis or Dissertation