9 papers
Twisted forms of classical hypersurfaces
Alvaro Liendo, Matías Vásquez
We count the twisted forms, over the field of real numbers and over finite fields, of the three classical families of smooth hypersurfaces with large automorphism group: the Fermat…
The Automorphism groups of zero-dimensional monomial algebras
Roberto DÃaz, Alvaro Liendo, Gonzalo Manzano-Flores +1
A monomial algebra B is defined as a quotient of a polynomial ring by a monomial ideal, which is an ideal generated by a finite set of monomials. In this paper, we determine the au…
Automorphisms of prime power order of weighted hypersurfaces
Alvaro Liendo, Ana Julisa Palomino
We study automorphisms of quasi-smooth hypersurfaces in weighted projective spaces, extending classical results for smooth hypersurfaces in projective space to the weighted setting…
Topologically integrable derivations and additive group actions on affine ind-schemes
Roberto Diaz, Adrien Dubouloz, Alvaro Liendo
We develop a theory of additive group actions on affine ind-schemes through a purely algebraic and topological framework. Affine ind-schemes are described via complete, second-coun…
Nash blowup fails to resolve singularities in dimensions four and higher
Federico Castillo, Daniel Duarte, Maximiliano Leyton-Ãlvarez +1
In this paper we show that iterating Nash blowups or normalized Nash blowups does not resolve the singularities of algebraic varieties of dimension four or higher over an algebraic…
Characteristic-free normalized Nash blowup of toric varieties
Federico Castillo, Daniel Duarte, Maximiliano Leyton-Ãlvarez +1
We introduce conditions on cones of normal toric varieties under which the polyhedron defining the normalized Nash blowup does not depend on the characteristic of the base field. A…