46 research outputs found
A generalized Bogomolov-Gieseker inequality for the three-dimensional projective space
A generalized Bogomolov-Gieseker inequality for tilt-stable complexes on a
smooth projective threefold was conjectured by Bayer, Toda, and the author. We
show that such inequality holds true in general, if it holds true when the
polarization is sufficiently small. As an application, we prove it for the
three-dimensional projective space.Comment: 17 pages, 4 figure
Classification of Poisson surfaces
We study complex projective surfaces admitting a Poisson structure. We prove
a classification theorem and count how many independent Poisson structures
there are on a given Poisson surface.Comment: LaTeX file, 8 pages; to be published in "Communications in
Contemporary Mathematics
Stability conditions on Kuznetsov components
We introduce a general method to induce Bridgeland stability conditions on
semiorthogonal decompositions. In particular, we prove the existence of
Bridgeland stability conditions on the Kuznetsov component of the derived
category of many Fano threefolds (including all but one deformation type of
Picard rank one), and of cubic fourfolds. As an application, in the appendix,
written jointly with Xiaolei Zhao, we give a variant of the proof of the
Torelli theorem for cubic fourfolds by Huybrechts and Rennemo.Comment: 52 pages. Appendix about the Torelli theorem for cubic fourfolds by
A. Bayer, M. Lahoz, E. Macri', P. Stellari, and X. Zhao. v2: main results
also for characteristic p; updated discussion about related wor
Derived categories and the genus of space curves
We generalize a classical result about the genus of curves in projective space by Gruson and Peskine to principally polarized abelian threefolds of Picard rank one. The proof is based on wall-crossing techniques for ideal sheaves of curves in the derived category. In the process, we obtain bounds for Chern characters of other stable objects such as rank two sheaves. The argument gives a proof for projective space as well. In this case these techniques also indicate an approach for a conjecture by Hartshorne and Hirschowitz and we prove first steps toward it. © Foundation Compositio Mathematica 2020