We study the singularity category of the triangle singularity f= xa+ yb+ zc, or S= k [x, y, z]/(f),
attached to the weighted projective line X, given by the weight triple (a, b, c), by investigating …

Weighted projective lines, introduced by Geigle and Lenzing in 1987, are important objects
in representation theory. They have tilting bundles, whose endomorphism algebras are the …

We study the four-dimensional superconformal\(\mathcal {N}= 2\) gauge theories
engineered by the Type IIB superstring on Arnold's 14 exceptional unimodal singularities …

We give a geometric model for the category of coherent sheaves over the weighted
projective line of type $(p, q) $ in terms of an annulus with marked points on its boundary …

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 …

We investigate group actions on the category of coherent sheaves over weighted projective
lines. We show that the equivariant category with respect to certain finite group action is …

This thesis studies weighted projective planes and their connection to threefold singularities.
In particular, we study the Veronese subring S→ 𝑥 of the ring S associated with the …

Supersymmetric N= 2 theories in four dimensions are an interesting laboratory to
understand Quantum Field Theory at strong coupling. In these theories many interesting …

We present a largely self contained account on the K-theory of a weighted smooth projective
curve over an algebraically closed field. In particular, we discuss the weighted version of …