This paper proposes some material towards a theory of general toric varieties without the
assumption of normality. Their combinatorial description involves a fan to which is attached …

We show that the Nash blowup of 2-generic determinantal varieties over fields of positive
characteristic is non-singular. We prove this in two steps. Firstly, we explicitly describe the …

The problem of resolution of singularities and its solution in various contexts can be traced
back to I. Newton and B. Riemann. This paper is an attempt to give a survey of the subject …

We develop a general theory of log spaces, in which one can make sense of the basic
notions of logarithmic geometry, in the sense of Fontaine-Illusie-Kato. Many of our general …

We initiate the study of the resolution of singularities properties of Nash blowups over fields
of prime characteristic. We prove that the iteration of normalized Nash blowups …

It has been recently shown that the iteration of Nash modification on not necessarily normal
toric varieties corresponds to a purely combinatorial algorithm on the generators of the …

We investigate the relation between essential divisors and F-blowups, in particular, address
the problem whether all essential divisors appear on the $ e $-th F-blowup for large enough …

We initiate the study of Nash blowups in prime characteristic. First, we show that a normal
variety is non-singular if and only if its Nash blowup is an isomorphism, extending a theorem …

We introduce a higher-order version of the tangent map of a morphism and find a matrix
representation. We then apply this matrix to solve a conjecture by Yasuda regarding the …

Factorization of the normalization of the Nash blowup of order n of A n by the minimal resolution
Page 1 Rev. Mat. Iberoam. (Online first) DOI 10.4171/RMI/1421 © 2023 Real Sociedad …