Generating functions for colored 3D Young diagrams and the Donaldson-Thomas invariants of orbifolds: With an appendix by Jim Bryan
2010 (English)In: Duke mathematical journal, ISSN 0012-7094, Vol. 152, no 1, 115-153 p.Article in journal (Refereed) Published
We derive two multivariate generating functions for three-dimensional (3D) Young diagrams (also called plane partitions). The variables correspond to a coloring of the boxes according to a finite Abelian subgroup G of SO (3). These generating functions turn out to be orbifold Donaldson-Thomas partition functions for the orbifold [C 3/G]. We need only the vertex operator methods of Okounkov, Reshetikhin, and Vafa for the easy case G = Z n; to handle the considerably more difficult case G = Z 2 × Z 2, we also use a refinement of the author's recent q-enumeration of pyramid partitions. In the appendix, we relate the diagram generating functions to the Donaldson-Thomas partition functions of the orbifold [C 3/G]. We find a relationship between the Donaldson-Thomas partition functions of the orbifold and its G-Hilbert scheme resolution. We formulate a crepant resolution conjecture for the Donaldson-Thomas theory of local orbifolds satisfying the hard Lefschetz condition.
Place, publisher, year, edition, pages
2010. Vol. 152, no 1, 115-153 p.
Gromov-Witten Theory, Plane Partitions, Curves
IdentifiersURN: urn:nbn:se:kth:diva-93332DOI: 10.1215/00127094-2010-009ISI: 000275813700004OAI: oai:DiVA.org:kth-93332DiVA: diva2:515692
QC 201206262012-04-142012-04-142012-06-26Bibliographically approved