Toric sheaves on weighted projective planes

We give an explicit description of toric sheaves on the weighted projective plane P(a, b, c) viewed as a toric Deligne-Mumford stack. The stack P(a, b, c) has an action of the torus T = C∗2 and by a toric sheaf we mean a coherent sheaf together with a lift of the torus action. The integers (a, b, c) are not necessarily chosen coprime or mutually coprime allowing for gerbe and root stack structures. This is a ﬁrst step in an attempt to give an explicit description of toric sheaves on any smooth toric Deligne-Mumford stack. Specializing the description to torsion free sheaves gives a combinatorial picture with various new features, which do not appear in the case of smooth toric varieties. As an application, we describe the ﬁxed point locus of the moduli scheme of stable rank 1 and 2 torsion free sheaves on P(a, b, c) with ﬁxed K-group

Từ khóa: Algebraic Geometry, High Energy Physics theory, toric sheaves, Toric sheaves on weighted projective planes, lý thuyết vật lý năng lựong cao, đại số hình học