92 citations · 253 across the 22 of their papers we have counts for
4 papers · 1 filter
A syzygetic approach to the smoothability of zero-dimensional schemes
Daniel Erman, Mauricio Velasco
We consider the question of which zero-dimensional schemes deform to a collection of distinct points; equivalently, we ask which Artinian k-algebras deform to a product of fields.…
A survey on Cox rings
Antonio Laface, Mauricio Velasco
We survey the construction of the Cox ring of an algebraic variety X and study the birational geometry of X when its Cox ring is finitely generated.
Cox rings of degree one del Pezzo surfaces
Damiano Testa, Anthony Várilly-Alvarado, Mauricio Velasco
Let X be a del Pezzo surface of degree one over an algebraically closed field (of any characteristic), and let Cox(X) be its total coordinate ring. We prove the missing case of a c…
Hilbert schemes of 8 points
Dustin A. Cartwright, Daniel Erman, Mauricio Velasco +1
The Hilbert scheme H^d_n of n points in A^d contains an irreducible component R^d_n which generically represents n distinct points in A^d. We show that when n is at most 8, the Hil…