A generalized Bogomolov–Gieseker inequality for the smooth quadric threefold

By Benjamin Schmidt. 2013

67 citations recorded by the source corpus.

We prove a generalized Bogomolov–Gieseker inequality as conjectured by Bayer, Macrì and Toda for the smooth quadric threefold. This implies the existence of a family of Bridgeland stability conditions.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/afcc59830e78792386caa62aafe9d7468798fe58

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Bridgeland Stability Conditions on Fano Threefolds (2016, methodology): “r any ;-stable object E2Coh(X) with ;(E) = 0 the inequality ch 2 3 (E) 2 6 H ch 1 (E) holds. The conjecture has been proved for P3 in [Mac14b] and for the smooth quadric hypersurface QˆP4 in [Sch14]. All other Fano threefolds of Picard rank one were handled in [Li15]. Finally, it is known to hold”
The space of stability conditions on abelian threefolds, and on some Calabi-Yau threefolds (2014, methodology): “4, and since the latter has been verified for P3 in [11,26], and for the quadric threefold in [39], it also applies in these two cases.”
Lectures on Bridgeland Stability (2016, methodology): “The first proof was in the case of P3 in [Mac14a] and a very similar proof worked for the smooth quadric hypersurface in P4 in [Sch14].”
Stability conditions on Fano threefolds of Picard number 1 (2015, background): “The case of P(3) and quadric 3-fold in P(4) has already been set up in [1, 9, 10] .”
Fourier-Mukai Transforms and Bridgeland Stability Conditions on Abelian Threefolds (2013, background): “This inequality has been shown to hold for three dimensional projective space (see [4] and [12]) and smooth quadric threefold (see [17]), and some progress has been made for more general threefolds (see [19] and [9]).”