19 citations · 57 across the 17 of their papers we have counts for
17 papers
Arcs on rational double points in arbitrary characteristic
Tommaso de Fernex, Shih-Hsin Wang
We prove that the Nash problem holds for two-dimensional rational double points in all characteristics. The proof is based on a direct computation of the families of arcs through t…
Relative Mather discrepancy on arc spaces
Tommaso de Fernex, Zach Mere
Given any generically étale morphism of varieties , we define the relative Mather discrepancy function on the arc space of the domain and show that thi…
The volume of a set of arcs on a variety
Tommaso de Fernex, Mircea Mustata
In this paper, we give a definition of volume for subsets in the space of arcs of an algebraic variety, and study its properties. Our main result relates the volume of a set of arc…
The dual complex of singularities
Tommaso de Fernex, János Kollár, Chenyang Xu
The dual complex of a singularity is defined, up-to homotopy, using resolutions of singularities. In many cases, for instance for isolated singularities, we identify and study a "m…
Rigidity properties of Fano varieties
Tommaso de Fernex, Christopher Hacon
We overview some recent results on Fano varieties giving evidence of their rigid nature under small deformations.
The Ascending Chain Condition for log canonical thresholds on l.c.i. varieties
Tommaso de Fernex, Mircea Mustata
Shokurov's ACC Conjecture says that the set of all log canonical thresholds on varieties of bounded dimension satisfies the Ascending Chain Condition. This conjecture was proved fo…