An explicit normal singular affine toric variety of dimension five in characteristic three has its normalized Nash blowup containing an open affine subset isomorphic to itself, yielding one-step counterexamples to the normalized Nash blowup conjecture in all dimensions five and higher.
Convex bodies and algebraic geometry: an introduction to the theory of toric varieties
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Determines the automorphism groups of zero-dimensional monomial algebras via explicit classification of homogeneous locally nilpotent derivations, extending to semigroup algebras.
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A one-step counterexample to the normalized Nash blowup conjecture
An explicit normal singular affine toric variety of dimension five in characteristic three has its normalized Nash blowup containing an open affine subset isomorphic to itself, yielding one-step counterexamples to the normalized Nash blowup conjecture in all dimensions five and higher.
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The Automorphism groups of zero-dimensional monomial algebras
Determines the automorphism groups of zero-dimensional monomial algebras via explicit classification of homogeneous locally nilpotent derivations, extending to semigroup algebras.