15 citations · 51 across the 7 of their papers we have counts for
8 papers
Donaldson-Thomas invariants of abelian threefolds and Bridgeland stability conditions
Georg Oberdieck, Dulip Piyaratne, Yukinobu Toda
We study the reduced Donaldson-Thomas theory of abelian threefolds using Bridgeland stability conditions. The main result is the invariance of the reduced Donaldson-Thomas invarian…
Stability Conditions Under the Fourier-Mukai Transforms on Abelian Threefolds
Dulip Piyaratne
We realize explicit symmetries of Bridgeland stability conditions on any abelian threefold given by Fourier-Mukai transforms. In particular, we extend the previous joint work with…
Stability conditions, Bogomolov-Gieseker type inequalities and Fano 3-folds
Dulip Piyaratne
We develop a framework to modify the Bogomolov-Gieseker type inequality conjecture introduced by Bayer-Macri-Toda, in order to construct a family of geometric Bridgeland stability…
Generalized Bogomolov-Gieseker type inequalities on Fano 3-folds
Dulip Piyaratne
We modify the conjectural Bogomolov-Gieseker type inequality introduced by Bayer, Macri and Toda to construct a family of geometric Bridgeland stability conditions on smooth projec…
Fourier-Mukai Transforms and Stability Conditions on Abelian Varieties
Dulip Piyaratne
This article is based on a talk given at the Kinosaki Symposium on Algebraic Geometry in 2015, about a work in progress. We describe a polarization on a derived equivalent abelian…
Moduli of Bridgeland semistable objects on 3-folds and Donaldson-Thomas invariants
Dulip Piyaratne, Yukinobu Toda
We show that the moduli stacks of Bridgeland semistable objects on smooth projective 3-folds are proper algebraic stacks of finite type, if they satisfy the Bogomolov-Gieseker (BG…
Fourier-Mukai Transforms and Bridgeland Stability Conditions on Abelian Threefolds II
Antony Maciocia, Dulip Piyaratne
We show that the conjectural construction proposed by Bayer, Bertram, Macrí and Toda gives rise to Bridgeland stability conditions for a principally polarized abelian three-fold wi…
Fourier-Mukai Transforms and Bridgeland Stability Conditions on Abelian Threefolds
Antony Maciocia, Dulip Piyaratne
We show that the construction of Bayer, Bertram, Macri and Toda gives rise to a Bridgeland stability condition on a principally polarized abelian threefold with Picard rank one by…