Deformations and simultaneous resolution of determinantal surfaces
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Date
2025-11-25
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Publisher
Oxford University Press
Abstract
This paper uses reconstruction algebras to construct simultaneous resolution of determinantal surfaces. The main new difference to the classical case is that, in addition to the quiver of the reconstruction algebra, certain non-commutative relations, namely those of the canonical algebra of Ringel, are required. All the relations of the reconstruction algebra except the canonical relation are then deformed, and these deformed relations together with variation of the geometric invariant theory (GIT) quotient achieve the simultaneous resolution.
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Keywords
Determinantal surfaces, Simultaneous resolution, Surface deformations, Algebraic geometry, Singularity analysis
Citation
Makonzi, B. (2025). Deformations and Simultaneous Resolution of Determinantal Surfaces. The Quarterly Journal of Mathematics, haaf044.