TOMMASO DE FERNEX

Professor - University of Utah

PUBLICATIONS

Nash blow-ups of jet schemes

(with R. Docampo)
submitted
arxiv
Jet closures and the local isomorphism problem

(with L. Ein and S. Ishii)
submitted
arxiv
Differentials on the arc space

(with R. Docampo)
submitted
arxiv
The space of arcs of an algebraic variety

to appear in the Proceedings of the 2015 Summer Institute on Algebraic Geometry
arxiv
Towards a link theoretic characterization of smoothness

(with Y.-C. Tu)
Math. Res. Lett. 24 (2017), 1239-1262
arxiv
Birational rigidity of singular Fano hypersurfaces

Ann. Sc. Norm. Super. Pisa, Cl. Sci. 17 (2017), 911-929
arxiv
Colength of a product of ideals

in appendix to: J. Kollár and A. Némethi, Dufree's conjecture on the signature of smoothings of surface singularities
Ann. Sci. École Norm. Sup. 50 (2017), 787-798
arxiv
The dual complex of singularities

(with J. Kollár and C. Xu)
in "Higher dimensional algebraic geometry" in honour of Professor Yujiro Kawamatas 60th birthday, 103–130, Adv. Stud. Pure Math. Vol. 74, 2017
arxiv
Terminal valuations and the Nash problem

(with R. Docampo)
Invent. Math. 203 (2016), 303-331
journal arxiv
The volume of a set of arcs on a variety

(with M. Mustata)
Rev. Roumaine Math. Pures Appl. 60 (2015), 375-401
special issue in honor of Lucian Badescu's 70th birthday
arxiv
Comparing multiplier ideals to test ideals on numerically Q-Gorenstein varieties

(with R. Docampo, S. Takagi and K. Tucker)
Bull. London Math. Soc. 47 (2015), 359-369
journal arxiv
Valuation spaces and multiplier ideals on singular varieties

(with S. Boucksom, C. Favre and S. Urbinati)
in "Recent Advances in Algebraic Geometry," volume in honor of Rob Lazarsfeld's 60th birthday, 29-51, London Math. Soc. Lecture Note Series, 2015
arxiv
Fano hypersurfaces and their birational geometry

in "Automorphisms in Birational and Affine Geometry," Levico Terme, Italy, October 2012, Springer Proceedings in Mathematics & Statistics, Vol. 79, 2014.
arxiv
Jacobian discrepancies and rational singularities

(with R. Docampo)
J. Eur. Math. Soc. 16 (2014), 165-199
journal arxiv
Three-dimensional counter-examples to the Nash problem

Compositio Math. 149 (2013), 1519-1534
journal arxiv
Birationally rigid hypersurfaces

Invent. Math. 192 (2013), 533-566
Erratum, Invent. Math. 203 (2016), 675-680
journal arxiv

journal arxiv
Rationality in families of threefolds

(with D. Fusi)
Rend. Circ. Mat. Palermo 62 (2013), 127–135
journal arxiv
The volume of an isolated singularity

(with S. Boucksom and C. Favre)
Duke Math. J. 161 (2012), 1455-1520
journal arxiv
Rigidity properties of Fano varieties

(with C. Hacon)
in Current Developments in Algebraic Geometry, MSRI Publications, Volume 59, 2011
journal arxiv
Deformations of canonical pairs and Fano varieties

(with C. Hacon)
J. reine angew. Math. 651 (2011), 97-126
journal arxiv
Log canonical thresholds on varieties with bounded singularities

(with L. Ein and M. Mustata)
in "Classification of algebraic varieties-Schiermonnikoog 2009" C. Faber, G. van der Geer, E. Looijenga editors, EMS Ser. Congr. Rep., Eur. Math. Soc., Zürich, 2011
journal arxiv
Shokurov's ACC Conjecture for log canonical thresholds on smooth varieties

(with L. Ein and M. Mustata)
Duke Math. J. 152 (2010), 93-114
journal arxiv
A vanishing theorem for log canonical pairs

(with L. Ein)
Amer. J. Math. 132 (2010), 1205-1221
journal arxiv
Singularities on normal varieties

(with C. Hacon)
Compositio Math. 145 (2009), 393-414
journal arxiv
Limits of log canonical thresholds

(with M. Mustata)
Ann. Sci. École Norm. Sup. 42 (2009), 493-517
journal arxiv
Ample subvarieties and rationally connected fibrations

(with M. Beltrametti and A. Lanteri)
Math. Ann. 341 (2008), 897-926
journal arxiv
Divisorial valuations via arcs

(with L. Ein and S. Ishii)
Publ. Res. Inst. Math. Sci. 44 (2008), 425-448
special issue in honor of Professor Hironaka's 70th birthday
journal arxiv
Higher cohomology of divisors on a projective variety

(with A. Kuronya and R. Lazarsfeld)
Math. Ann. 337 (2007), 443-455
journal arxiv
Stringy Chern classes of singular varieties

(with E. Lupercio, T. Nevins and B. Uribe)
Adv. Math. 208 (2007), 597-621
journal arxiv
A localization principle for orbifold theories

(with E. Lupercio, T. Nevins and B. Uribe)
in "Recent Developments in Algebraic Topology", A. Adem et al. eds., Proceedings for the Conference in honor of the 70th birthday of S. Gitler, 113-133. Contemp. Math. 407, Amer. Math. Soc., Providence, RI, 2006
arxiv
Length, multiplicity, and multiplier ideals

Trans. Amer. Math. Soc. 358 (2006), 3717-3731
journal arxiv
Bad loci of free linear systems

(with A. Lanteri)
Adv. Geom. 6 (2006), 93-107
journal arxiv
Negative curves on very general blow-ups of P^2

in "Projective Varieties with Unexpected Properties", M. Beltrametti et al. eds., A Volume in Memory of Giuseppe Veronese, 199-207, de Gruyter, Berlin, 2005
journal arxiv
Multiplicities and log canonical threshold

(with L. Ein and M. Mustata)
J. Algebraic Geom. 13 (2004), 603-615
journal arxiv
On planar Cremona maps of prime order

Nagoya Math. J. 174 (2004), 1-28
journal arxiv
Bounds on log canonical thresholds with application to birational rigidity

(with L. Ein and M. Mustata)
Math. Res. Lett. 10 (2003), 219-236
journal arxiv
Resolution of indeterminacy of pairs

(with L. Ein)
in "Algebraic Geometry", M. Beltrametti et al. eds., A Volume in Memory of Paolo Francia, 165-177, de Gruyter, Berlin, 2002
journal
Ample vector bundles and intrinsic quadric fibrations over irrational curves

Matematiche (Catania) 55 (2000), 205-222
journal
Ample vector bundles and del Pezzo manifolds

(with A. Lanteri)
Kodai Math. J. 22 (1999), 85-100
journal
Ample vector bundles with sections vanishing along conic fibrations over curves

Collect. Math. 49 (1998), 67-79
journal

OTHER WRITINGS

Vanishing theorems and singularities in birational geometry

(with L. Ein and M. Mustata)
book in preparation
On the Mori cone of blow-ups of the plane

unpublished
arxiv
Lectures on relative motivic integration, MacPherson's transformation, and stringy Chern classes

lectures held during the VIGRE Mini-Course on Arc Spaces and Motivic Integration, University of Utah, May 2005
draft
research partially suppported by the National Science Foundation