37 citations · 136 across the 12 of their papers we have counts for
11 papers · 1 filter
Derived jet and arc spaces
Roi Docampo, Lance Edward Miller, C. Eric Overton-Walker
We study jet schemes and arc spaces in the context of derived algebraic geometry. Explicitly, we consider the jet and arc functors in the category of schemes and study their animat…
On arc fibers of morphisms of schemes
Christopher Chiu, Tommaso de Fernex, Roi Docampo
Given a morphism of schemes over a field, we prove several finiteness results about the fibers of the induced map on arc spaces $f_\infty \colon X_\infty \to Y_\…
Embedding codimension of the space of arcs
Christopher Chiu, Tommaso de Fernex, Roi Docampo
We introduce a notion of embedding codimension of an arbitrary local ring, establish some general properties, and study in detail the case of arc spaces of schemes of finite type o…
Nash blow-ups of jet schemes
Tommaso de Fernex, Roi Docampo
Given an arbitrary projective birational morphism of varieties, we provide a natural and explicit way of constructing relative compactifications of the maps induced on the main com…
Differentials on the arc space
Tommaso de Fernex, Roi Docampo
The paper provides a description of the sheaves of Kähler differentials of the arc space and jet schemes of an arbitrary scheme where these sheaves are computed directly from the s…
The arc space of the Grassmannian
Roi Docampo, Antonio Nigro
We study the arc space of the Grassmannian from the point of view of the singularities of Schubert varieties. Our main tool is a decomposition of the arc space of the Grassmannian…
A boundedness conjecture for minimal log discrepancies on a fixed germ
Mircea Mustata, Yusuke Nakamura
We consider the following conjecture: on a klt germ (X,x), for every finite set I there is a positive integer N with the property that for every R-ideal J on X with exponents in I,…
Terminal valuations and the Nash problem
Tommaso de Fernex, Roi Docampo
Let X be an algebraic variety of characteristic zero. Terminal valuations are defined in the sense of the minimal model program, as those valuations given by the exceptional diviso…
Comparing multiplier ideals to test ideals on numerically Q-Gorenstein varieties
Tommaso de Fernex, Roi Docampo, Shunsuke Takagi +1
We show that the reduction to positive characteristic of the multiplier ideal in the sense of de Fernex and Hacon agrees with the test ideal for infinitely many primes, assuming th…
Jacobian discrepancies and rational singularities
Tommaso de Fernex, Roi Docampo
Inspired by several works on jet schemes and motivic integration, we consider an extension to singular varieties of the classical definition of discrepancy for morphisms of smooth…
Arcs on Determinantal Varieties
Roi Docampo
We study arc spaces and jet schemes of generic determinantal varieties. Using the natural group action, we decompose the arc spaces into orbits, and analyze their structure. This a…