88 citations · 344 across the 26 of their papers we have counts for
31 papers
Families of jets of arc type and higher (co)dimensional Du Val singularities
Tommaso de Fernex, Shih-Hsin Wang
Families of jets through singularities of algebraic varieties are here studied in relation to the families of arcs originally studied by Nash. After proving a general result relati…
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_\…
Birational rigidity and K-stability of Fano hypersurfaces with ordinary double points
Tommaso de Fernex
Extending previous results, we prove that for all hypersurfaces of degree in with isolated ordinary double points are birational superrigid and…
Motivic integration on Berkovich spaces
Tommaso de Fernex, Chung Ching Lau
We define a motivic measure on the Berkovich analytification of an algebraic variety defined over a trivially valued field, and introduce motivic integration in this setting. The c…
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…
Grothendieck--Lefschetz for ample subvarieties
Tommaso de Fernex, Chung Ching Lau
We establish a Grothendieck--Lefschetz theorem for smooth ample subvarieties of smooth projective varieties over an algebraically closed field of characteristic zero and, more gene…
Smooth solutions to the complex Plateau problem
Tommaso de Fernex
Building on work of Du, Gao, and Yau, we give a characterization of smooth solutions, up to normalization, of the complex Plateau problem for strongly pseudoconvex Calabi--Yau CR m…
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…
Jet closures and the local isomorphism problem
Tommaso de Fernex, Lawrence Ein, Shihoko Ishii
If a morphism of germs of schemes induces isomorphisms of all local jet schemes, does it follow that the morphism is an isomorphism? This problem is called the local isomorphism pr…
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…
Towards a link theoretic characterization of smoothness
Tommaso de Fernex, Yu-Chao Tu
A theorem of Mumford states that, on complex surfaces, any normal isolated singularity whose link is diffeomorphic to a sphere is actually a smooth point. While this property fails…
The space of arcs of an algebraic variety
Tommaso de Fernex
The paper surveys several results on the topology of the space of arcs of an algebraic variety and the Nash problem on the arc structure of singularities.
Erratum to: Birationally rigid hypersurfaces
Tommaso de Fernex
This note points out a gap in the proof of the main theorem of the article "Birationally rigid hypersurfaces" published in Invent. Math. 192 (2013), 533-566, and provides a new pro…
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,…
Durfee's conjecture on the signature of smoothings of surface singularities
Tommaso de Fernex, János Kollár, András Némethi
In 1978 Durfee conjectured various inequalities between the signature and the geometric genus of a normal surface singularity. Since then a few counter examples have been found and…
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…
Fano hypersurfaces and their birational geometry
Tommaso de Fernex
We survey some results on the nonrationality and birational rigidity of certain hypersurfaces of Fano type. The focus is on hypersurfaces of Fano index one, but hypersurfaces of hi…
Valuation spaces and multiplier ideals on singular varieties
Sébastien Boucksom, Tommaso de Fernex, Charles Favre +1
We generalize to all normal complex algebraic varieties the valuative characterization of multiplier ideals due to Boucksom-Favre-Jonsson in the smooth case. To that end, we extend…
Birational rigidity of singular Fano hypersurfaces
Tommaso de Fernex
We establish birational superrigidity for a large class of singular projective Fano hypersurfaces of index one. In the special case of isolated singularities, our result applies fo…
Three-dimensional counter-examples to the Nash problem
Tommaso de Fernex
The Nash problem asks about the existence of a correspondence between families of arcs through singularities of complex varieties and certain types of divisorial valuations. It has…
Rationality in families of threefolds
Tommaso de Fernex, Davide Fusi
We prove that in a family of projective threefolds defined over an algebraically closed field, the locus of rational fibers is a countable union of closed subsets of the locus of s…
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…
The volume of an isolated singularity
Sebastien Boucksom, Tommaso De Fernex, Charles Favre
We introduce a notion of volume of a normal isolated singularity that generalizes Wahl's characteristic number of surface singularities to arbitrary dimensions. We prove a basic mo…