Collections > UNC Chapel Hill Undergraduate Honors Theses Collection > BRIDGELAND STABILITY AND NON-COMMUTATIVE TORI

The goal of this paper is to look at strong theorems relating thedifferential geometry of vector bundles to their stability in an algebraicsense and start to see how these theorems might be extended to morerefined notions of stability. Bridgeland stability is in particular definedfor objects in the derived category D(X) = D b (Coh(X)) for a varietyX. We will show in Corollary 9.1 that, at least when X is an ellipticcurve, there is a heart of a bounded t-structure in D(X) which isequivalent to a category of vector bundles on a non-commutative torusrelated to X based on a description of this latter category by Polishchukand Schwarz 17. Under this equivalence, Bridgeland stable objectscorrespond to bundles with special connections.