Highlight
Federico Castillo, Daniel Duarte, Maximiliano Leyton-Alvarez and Alvaro Liendo. Nash blowup fails to resolve singularities in dimensions four and higher. Annals of Mathematics 203 (2026), no. 2, 677-694. arXiv:2409.19767
This result, which answers Nash's question negatively in dimension four and higher, was made possible by a computational effort developed for an earlier version of this project.
Papers
Federico Castillo, Daniel Duarte, Maximiliano Leyton-Alvarez and Alvaro Liendo. Characteristic-free normalized Nash blowup of toric varieties. Journal of the London Mathematical Society 114 (2026), no. 4. arXiv:2501.09811
Federico Castillo, Daniel Duarte, Maximiliano Leyton-Alvarez and Alvaro Liendo. On a computational approach to the Nash blowup problem. Experimental Mathematics (2026), published online 28 October 2026. arXiv:2511.17862
Alvaro Liendo and Ana Julisa Palomino. Automorphisms of prime power order of weighted hypersurfaces. Transformation Groups (2026). arXiv:2507.13538
Federico Castillo, Daniel Duarte, Maximiliano Leyton-Alvarez and Alvaro Liendo. Non-normalized Nash blowup fails to resolve singularities in dimension three. To appear in Compositio Mathematica. arXiv:2511.01772
Roberto Díaz, Alvaro Liendo, Gonzalo Manzano-Flores and Andriy Regeta. The automorphism groups of zero-dimensional monomial algebras. To appear in Annales de l'Institut Fourier. arXiv:2408.02197
Preprints
Jorge Duque Franco, Alvaro Liendo and Pedro Montero. Automorphisms and Hodge isometries of surfaces with K2 = pg = 1. Preprint (2026). arXiv:2610.33364
Alvaro Liendo and Matías Vásquez. Twisted forms of classical hypersurfaces. Preprint (2026). arXiv:2608.13896
Alvaro Liendo, Ana Julisa Palomino and Gonzalo Rodríguez. A one-step counterexample to the normalized Nash blowup conjecture. Preprint (2026). arXiv:2604.07519
Roberto Díaz, Adrien Dubouloz and Alvaro Liendo. Topologically integrable derivations and additive group actions on affine ind-schemes. Preprint (revised 2026). arXiv:2012.14302
Ghadi Abdallah, Maximiliano Leyton-Alvarez, Bassam Mourad and Hussein Mourtada. Jet schemes, Newton polygons and continued fractions. Preprint (2025). arXiv:2509.06095