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Algebraic Geometry: "Bogomolov-Gieseker Inequalities and Stability Conditions"

Dr. Cristian Martinez, UC Santa Barbara

Thursday, February 2, 2017
  1:10–2 p.m.


Location: Surge Building 268
  Parking Information

Category: Seminar

Description: Given a Chern character v and an ample class H on a smooth projective complex surface, there is a distinguished open set of stability conditions so that the only semistable objects of type v are coherent sheaves that are Gieseker semistable with respect to H. Moving away from this chamber to its boundary corresponds to a contraction of the Gieseker moduli. This, for instance, accounts for all smooth MMPs on surfaces. One of the key ingredients in the construction of stability conditions on surfaces is the Bogomolov-Gieseker inequality on the Chern character of a semistable sheaf. On some threefolds a generalized inequality is satisfied by a class of "semistable" complexes, allowing for the construction of stability conditions. In this talk I will explore some of the ideas above and show a class of stable complexes violating the generalized Bogomolov-Gieseker inequality on blow-ups of smooth threefolds.

Additional Information: AG Seminar

Open to: General Public
Admission: Free
Sponsor: Mathematics

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