English

Deformations and Simultaneous Resolution of Determinantal Surfaces

Algebraic Geometry 2025-11-03 v2 Representation Theory

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 noncommutative 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 GIT quotient achieve the simultaneous resolution.

Keywords

Cite

@article{arxiv.2309.02982,
  title  = {Deformations and Simultaneous Resolution of Determinantal Surfaces},
  author = {Brian Makonzi},
  journal= {arXiv preprint arXiv:2309.02982},
  year   = {2025}
}

Comments

15 pages, Conjecture 5.2 restated, typos corrected

R2 v1 2026-06-28T12:14:15.132Z