DG quivers of smooth rational surfaces
Agnieszka Bodzenta
TL;DR
This paper computes the differential graded (DG) quivers associated with full exceptional collections of line bundles on smooth rational surfaces, including canonical DG algebras of smooth toric surfaces, advancing understanding of their algebraic structures.
Contribution
It introduces a method to calculate DG quivers for full exceptional collections on smooth rational surfaces, extending to canonical DG algebras of smooth toric surfaces.
Findings
Computed DG quivers for full exceptional collections on smooth rational surfaces.
Derived canonical DG algebras for smooth toric surfaces.
Provided explicit algebraic structures for these surfaces.
Abstract
Let X be a smooth rational surface. We calculate a DG quiver of a full exceptional collection of line bundles on X obtained by an augmentation from a strong exceptional collection on the minimal model of X. In particular, we calculate canonical DG algebras of smooth toric surfaces.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Algebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology