For a trivial elliptic fibration $$X=C \times S$$X=C×S with C an elliptic curve and S a projective K3 surface of Picard rank 1, we study how various notions of stability behave under the… Expand

In this article, we treat stability conditions in the sense of King, Bridgeland and Bayer in a single framework. Following King, we begin with weight functions on a triangulated category, and… Expand

On a Weierstrass elliptic surface $X$, we define a `limit' of Bridgeland stability conditions, denoted as $Z^l$-stability, by varying the polarisation along a curve in the ample cone. We describe… Expand

We define the notion of a holomorphic bundle on the noncommutative toric orbifold T θ/G associated with an action of a finite cyclic group G on an irrational rotation algebra. We prove that the… Expand

We study the Clifford type inequality for a particular type of curves $$C_{2,2,5}$$C2,2,5, which are contained in smooth quintic threefolds. This allows us to prove some stronger Bogomolov–Gieseker… Expand

Needless to say, tlie prototype of classification theory of varieties is tlie classical classification theory of algebraic surfaces by the Italian school, enriched by Zariski, Kodaira and others. Let… Expand