Bridgeland stability of line bundles on smooth projective surfaces
Date
2014
Authors
Miles, Eric W., author
Cavalieri, Renzo, advisor
Achter, Jeff, committee member
Peterson, Chris, committee member
Prasad, Ashok, committee member
Pries, Rachel, committee member
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Abstract
Bridgeland Stability Conditions can be thought of as tools for creating and varying moduli spaces parameterizing objects in the derived category of a variety X. Line bundles on the variety are fundamental objects in its derived category, and we characterize the Bridgeland stability of line bundles on certain surfaces. Evidence is provided for an analogous characterization in the general case. We find stability conditions for P1 × P1 which can be seen as giving the stability of representations of quivers, and we deduce projective structure on the Bridgeland moduli spaces in this situation. Finally, we prove a number of results on objects and a construction related to the quivers mentioned above.
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Subject
line bundle
surface
stability condition