BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Artan Sheshmani (Harvard University Center for Mathematical scienc es and Applications) DTSTART:20201210T150000Z DTEND:20201210T160000Z DTSTAMP:20260423T021242Z UID:ZAG/76 DESCRIPTION:Title: DT invariants from Gerstenhaber-BV structures\, and degeneration technique\nby Artan Sheshmani (Harvard University Center for Mathematical sciences and Applications) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nA bstract\nWe discuss Donaldson-Thomas (DT) invariants of torsion sheaves wi th 2 dimensional support on a smooth projective surface in an ambient non- compact Calabi Yau fourfold given by the total space of a rank 2 bundle on the surface. We prove that in certain cases\, when the rank 2 bundle is c hosen appropriately\, the universal truncated Atiyah class of these codime nsion 2 sheaves reduces to one\, defined over the moduli space of such she aves realized as torsion codimension 1 sheaves in a noncompact divisor (th reefold) embedded in the ambient fourfold. Such reduction property of univ ersal Atiyah class enables us to relate our fourfold DT theory to a reduce d DT theory of a threefold and subsequently then to the moduli spaces of s heaves on the base surface. We finally make predictions about modularity o f such fourfold invariants when the base surface is an elliptic K3. There are connections between these invariants and birational properties of the base surface which we will discuss if time permits.\n LOCATION:https://researchseminars.org/talk/ZAG/76/ END:VEVENT END:VCALENDAR