Explanipedia

The heart fan of an abelian category Open

Nathan Broomhead, David Pauksztello, David Ploog, Jon Woolf · 2023

We apply convex geometry (cones, fans) to homological input (abelian categories, hearts of bounded t-structures) to construct a new invariant of an abelian category, its heart fan. This can be viewed as a `universal phase diagram' for Brid…

Partial compactification of stability manifolds by massless semistable objects Open

Nathan Broomhead, David Pauksztello, David Ploog, Jon Woolf · 2022

We introduce two partial compactifications of the space of Bridgeland stability conditions of a triangulated category. First we consider lax stability conditions where semistable objects are allowed to have mass zero but still have a phase…

Functorially finite hearts, simple-minded systems in negative cluster categories, and noncrossing partitions Open

Raquel Coelho Simões, David Pauksztello, David Ploog · 2022

Let $Q$ be an acyclic quiver and $w \geqslant 1$ be an integer. Let $\mathsf {C}_{-w}({\mathbf {k}} Q)$ be the $(-w)$ -cluster category of ${\mathbf {k}} Q$ . We show that there is a bijection between simple-minded collections in $\mathsf …

Жесткие дивизоры на поверхностях Open

Andreas Hochenegger, David Ploog · 2020

Рассматриваются эффективные дивизоры $D$ на поверхностях, удовлетворяющие условиям $H^0(\mathcal{O}_D)=\Bbbk$ и $H^1(\mathcal{O}_D)=H^0(\mathcal{O}_D(D))=0$. Получена численная характеризация таких дивизоров и в общем случае изучены их сво…

Displaying the cohomology of toric line bundles Open

Klaus Altmann, David Ploog · 2019

There is a standard approach to calculate the cohomology of torus-invariant sheaves on a toric variety via the simplicial cohomology of the associated subsets of the space of 1-parameter subgroups of the torus. For a line bundle represente…

Derived categories of resolutions of cyclic quotient singularities Open

Andreas Krug, David Ploog, Pawel Sosna · 2017

For a cyclic group $G$ acting on a smooth variety $X$ with only one character occurring in the $G$-equivariant decomposition of the normal bundle of the fixed point locus, we study the derived categories of the orbifold $[X/G]$ and the blo…

Stability of Picard sheaves for vector bundles on curves Open

Georg Hein, David Ploog · 2016

Discrete derived categories I: homomorphisms, autoequivalences and t-structures Open

Nathan Broomhead, David Pauksztello, David Ploog · 2016

38 pages, many figures. v2: 47 pages, main results unchanged;\n presentation, proofs and pictures improved; additional content in Section 3\n and Appendix B

Discrete derived categories II: the silting pairs CW complex and the stability manifold Open

Nathan Broomhead, David Pauksztello, David Ploog · 2016

27 pages, 3 figures; second version incorporates many improvements\n thanks to the anonymous referee; to be published in Journal of the LMS

Der Mathematikkreis – kompetenzorientiertes Erarbeiten mathematischer Fragen mit drei- bis zehnjährigen Kindern Open

Christine Günther, David Ploog, Bernd Wollring · 2016

David Ploog YOU? Author Swipe