On stability conditions for the quintic threefold
TLDR
In this paper, the Bogomolov-Gieseker type inequalities for Chern characters of stable sheaves and tilt-stable objects on smooth quintic three-folds were studied.Abstract:
We study the Clifford type inequality for a particular type of curves $$C_{2,2,5}$$
, which are contained in smooth quintic threefolds. This allows us to prove some stronger Bogomolov–Gieseker type inequalities for Chern characters of stable sheaves and tilt-stable objects on smooth quintic threefolds. Employing the previous framework by Bayer, Bertram, Macri, Stellari and Toda, we construct an open subset of stability conditions on every smooth quintic threefold in $$\mathbf {P}^4_{\mathbb {C}}$$
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Citations
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Stability conditions in families
Arend Bayer,Martí Lahoz,Martí Lahoz,Emanuele Macrì,Emanuele Macrì,Howard Nuer,Howard Nuer,Alexander Perry,Alexander Perry,Paolo Stellari +9 more
TL;DR: In this article, the authors develop a theory of Bridgeland stability conditions and moduli spaces of semistable objects for a family of varieties, and show that such a structure exists whenever stability conditions are known to exist on the fibers, which leads to the extension of theorems by Addington-Thomas and Huybrechts on the derived category of special cubic fourfolds, and to the construction of an infinite series of unirational locally complete families of polarized hyperkahler manifolds of K3 type.
Journal ArticleDOI
Some Remarks on Fano Three-Folds of Index Two and Stability Conditions
Laura Pertusi,Song Yang +1 more
TL;DR: In this article, it was shown that ideal sheaves of lines in a Fano threefold of Picard rank one and index two are stable objects in the Kuznetsov component with respect to the stability conditions constructed by Bayer, Lahoz, Macri and Stellari.
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Stability and the deformed Hermitian-Yang-Mills equation
Tristan C. Collins,Yun Shi +1 more
TL;DR: The role of geometric invariant theory (GIT) in approaching the solvability of the deformed Hermitian-Yang-Mills (dHYM) equation was discussed in this paper.
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Moduli spaces on the Kuznetsov component of Fano threefolds of index 2
TL;DR: In this paper, the authors associate objects in the Kuznetsov component of a Fano threefold $Y$ of index 2 and Picard rank 1 are del Pezzo surfaces, and their Picard group is related to a root system.
Journal ArticleDOI
Stability conditions on threefolds with nef tangent bundles
TL;DR: In this paper, the Bogomolov-Gieseker type inequality conjecture for three-folds with tangent bundles was shown to hold for all three-fold bundles.
References
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TL;DR: In this paper, the authors introduce the notion of a stability condition on a triangulated category and prove a deformation result which shows that the space with its natural topology is a manifold, possibly infinite-dimensional.
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