Browsing Mathematics Theses and Dissertations by Author "Polishchuk, Alexander"
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Fisette, Robert (University of Oregon, 2012)[more][less]Polishchuk, Alexander Fisette, Robert Fisette, Robert 20121026T03:58:22Z 20121026T03:58:22Z 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 A1structure, which demonstrates that A1structures on B are finitely determined for curves of arbitrary genus. When the curve is taken over C and g = 1, we amend an explicit A1structure 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 jinvariant of the curve. When g 2, we use Massey products in Db(X) to show that in the A1structure 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. Ainfinity Curve Elliptic curve Hochschild cohomology jinvariant The Ainfinity Algebra of a Curve and the Jinvariant Electronic Thesis or Dissertation

Platt, David (University of Oregon, October 3, 2013)[more][less]Polishchuk, Alexander Platt, David 20131003T23:32:01Z 20131003T23:32:01Z 20131003 http://hdl.handle.net/1794/13244 We give a formula for the Chern character on the DG category of global matrix factorizations on a smooth scheme $X$ with superpotential $w\in \Gamma(\O_X)$. Our formula takes values in a Cech model for Hochschild homology. Our methods may also be adapted to get an explicit formula for the Chern character for perfect complexes of sheaves on $X$ taking values in right derived global sections of the DeRham algebra. Along the way we prove that the DG version of the Chern Character coincides with the classical one for perfect complexes. en_US University of Oregon All Rights Reserved. Chern Character Matrix Factorizations Noncommutative Geometry Chern Character for Global Matrix Factorizations Electronic Thesis or Dissertation Ph.D. doctoral Department of Mathematics University of Oregon
Now showing items 12 of 2