4 papers
Effective resolution of singularities
Edward Bierstone, Dima Grigoriev, Pierre D. Milman +1
Consider a projective variety (over an algebraically closed field of characteristic zero), together with a (reduced) simple normal crossings divisor $E \su…
Valuations, bijections, and bases
Arkady Berenstein, Dima Grigoriev
The aim of this paper is to build a theory of commutative and noncommutative {\it injective} valuations of various algebras (including algebras with zero divisors). The targets of…
Degree of 1-dimensional tropical prevariety
Dima Grigoriev
For a tropical prevariety $V\subset \RR^n$ (being a finite union of rational polyhedra) we define a tropical Hilbert function to be the maximal number of tropically indep…
Minimal solutions of tropical linear differential systems
Dima Grigoriev, Cristhian Garay López
We introduce and study minimal (with respect to inclusion) solutions of systems of tropical linear differential equations. We describe the set of all minimal solutions for a single…