Related papers: Tilting Objects via Recollements and $p$-Cycles on…

We calculate a semi-orthogonal decomposition of the bounded derived category of coherent sheaves on P(1,1,1,3) using a tilting bundle.

We show that one can achieve transversality for lifts of holomorphic disks to a projectivized vector bundle by locally enlarging the structure group and considering the action of gauge transformations on the almost complex structure, which…

We construct vector-valued modular forms on moduli spaces of curves and abelian varieties using effective divisors in projectivized Hodge bundles over moduli of curves. Cycle relations tell us the weight of these modular forms. In…

We establish connections between silting and tilting objects in an abelian category $\mathcal{B}$ and those in a cleft extension $\mathcal{A}$ of $\mathcal{B}$, which provides a method for constructing more silting and tilting objects. Then…

In a triangulated category T with a pair of triangulated subcategories X and Y, one may consider the subcategory of extensions X*Y. We give conditions for X*Y to be triangulated and use them to provide tools for constructing stable…

Let $\mathbb{X}$ be a Geigle-Lenzing projective plane of type $(2,2,2,p)$ and $\mathsf{coh} \mathbb{X}$ the category of coherent sheaves on $\mathbb{X}$. This paper is devoted to study ACM tilting bundles over $\mathbb{X}$, that is, tilting…

For any truncated path algebra $\Lambda$, we give a structural description of the modules in the categories ${\cal P}^{<\infty}(\Lambda\text{-mod})$ and ${\cal P}^{<\infty}(\Lambda\text{-Mod})$, consisting of the finitely generated (resp.…

Triangle presentations are combinatorial structures on finite projective geometries which characterize groups acting simply transitively on the vertices of a locally finite building of type $\tilde{\text{A}}_{n-1}$ ($n\ge3$). From a type…

This paper classifies all the tilting bundles in the category of coherent sheaves on the weighted projective line of weight type $(2, 2, n)$, and investigates the abelianness of the "missing part" from the category of coherent sheaves to…

We present a geometric model for the category of vector bundles over the weighted projective line of type (2,2,n). This model is based on the orbit space of an infinite marked strip under a specific group action. We establish a bijection…

We prove results concerning the specialisation of torsion line bundles on a variety $V$ defined over $\mathbb{Q}$ to ideal classes of number fields. This gives a new general technique for constructing and counting number fields with large…

Let $X$ be any rational surface. We construct a tilting bundle $T$ on $X$. Moreover, we can choose $T$ in such way that its endomorphism algebra is quasi-hereditary. In particular, the bounded derived category of coherent sheaves on $X$ is…

It is known that a tilting generator on an algebraic variety $X$ gives a derived equivalence between $X$ and a certain non-commutative algebra. In this paper, we explain a method to construct a tilting generator from an ample line bundle,…

This paper endeavors to explore certain distinguished modules and subcategories within mod$\Lambda$. Let $\mathrm{proj}\mbox{-}\Lambda$ denote the category of all finitely generated projective $\Lambda$-modules and define…

These notes provide a description of the abelian categories that arise as categories of coherent sheaves on weighted projective lines. Two different approaches are presented: one is based on a list of axioms and the other yields a…

This paper presents a robotic in-hand manipulation technique that can be applied to pick an object too large to grasp in a prehensile manner, by taking advantage of its contact interactions with a curved, passive end-effector, and two flat…

In this article we introduce a new class of non-commutative projective curves and show that in certain cases the derived category of coherent sheaves on them has a tilting complex. In particular, we prove that the right bounded derived…

We show that a tilting module over the endomorphism algebra of a cluster-tilting object in a 2-Calabi-Yau triangulated category lifts to a cluster-tilting object in this 2-Calabi-Yau triangulated category. This generalizes a recent work of…

Recent results by Keller and Nicol{\'a}s and by Koenig and Yang have shown bijective correspondences between suitable classes of t-structures and co-t-structures with certain objects of the derived category: silting objects. On the other…

A triangulated category $\mathcal{T}$ whose suspension functor $\Sigma$ satisfies $\Sigma^m \simeq \mathrm{Id}_{\mathcal{T}}$ as additive functors is called an $m$-periodic triangulated category. Such a category does not have a tilting…