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Stability Conditions on Threefolds and Space Curves

Schmidt, Benjamin
http://rave.ohiolink.edu/etdc/view?acc_num=osu1460542777

Abstract Details

2016, Doctor of Philosophy, Ohio State University, Mathematics.
This thesis investigates both constructions and applications of Bridgeland stability conditions on smooth complex projective varieties of dimension three. A conjectural construction of stability condition on threefolds due to Bayer, Macr\`i and Toda will be proven for the smooth quadric threefold and analogies to the proof for three-dimensional projective space will be pointed out. This implies the existence of a large family of Bridgeland stability conditions. Moreover, we will give a counterexample to the conjecture for the blow up of three dimensional projective space in a point. In between slope stability and Bridgeland stability there is the notion of tilt stability. Computations in it are similar to those for Bridgeland stability on surfaces. A technique to translate computations in tilt stability to wall crossings in Bridgeland stability will be developed. The author computes first examples of wall crossing behaviour in three dimensional projective space. In particular, for Hilbert schemes of curves such as twisted cubics or complete intersection curves of the same degree, two chambers in the stability manifold are described where the moduli space is given by a smooth projective irreducible variety respectively the Hilbert scheme. In the cases of twisted cubics and elliptic quartics, all walls and moduli spaces on a path between those two chambers are computed. This recovers former results about the geometry of these spaces.
David Anderson (Advisor)
Emanuele Macri (Committee Member)
Herbert Clemens (Committee Member)
James Cogdell (Committee Member)
118 p.
Mathematics
Algebraic Geometry, Bridgeland Stability Conditions, Derived Categories, Threefolds, Hilbert Schemes of Curves

Recommended Citations

Citations

  • Schmidt, B. (2016). Stability Conditions on Threefolds and Space Curves [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1460542777

    APA Style (7th edition)

  • Schmidt, Benjamin. Stability Conditions on Threefolds and Space Curves. 2016. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1460542777.

    MLA Style (8th edition)

  • Schmidt, Benjamin. "Stability Conditions on Threefolds and Space Curves." Doctoral dissertation, Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1460542777

    Chicago Manual of Style (17th edition)

osu1460542777
752
© 2016, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.