Tommaso de Fernex

TOMMASO DE FERNEX

PUBLICATIONS

Families of jets of arc type and higher (co)dimensional Du Val singularities (with S.-H. Wang) C. R. Math. Acad. Sci. Paris, 362 (2024), 119-139, special issue S1 “Complex algebraic geometry, in memory of Jean-Pierre Demailly”	arxiv
On arc fibers of morphisms of schemes (with C. Chiu and R. Docampo) J. Eur. Math. Soc. (JEMS) (2024), published online first, DOI 10.4171/JEMS/1500	arxiv
Motivic integration on Berkovich spaces over trivially valued fields (with C. C. Lau) to appear in Higher Dimensional Algebraic Geometry, a volume dedicated to Vyacheslav Shokurov on the occasion of his 70th birthday, Cambridge Univ. Press	arxiv
Birational rigidity and K-stability of Fano hypersurfaces with ordinary double points Rend. Circ. Mat. Palermo 72 (2023), 1049-1065	journal arxiv
Embedding codimension of the space of arcs (with C. Chiu and R. Docampo) Forum Math. Pi 10 (2022), e4 1-37	journal arxiv
Extending rationally connected fibrations from ample subvarieties (with C. C. Lau) Manuscripta Math. 169 (2022), 19–32	journal arxiv
Grothendieck-Lefschetz for ample subvarieties (with C. C. Lau) Math. Z. 300 (2022), 3319–3336 The geometry of algebraic varieties: special issue in honour of Olivier Debarre	journal arxiv
Smooth solutions to the complex Plateau problem J. Differential Geom. 118 (2021), 297-312	journal arxiv
Differentials on the arc space (with R. Docampo) Duke Math. J. 169 (2020), 353-396	journal arxiv
Nash blow-ups of jet schemes (with R. Docampo) Ann. Inst. Fourier 69 (2019), 2577-2588	journal arxiv
Jet closures and the local isomorphism problem (with L. Ein and S. Ishii) J. Algebra 501 (2018), 166-181	journal arxiv
The space of arcs of an algebraic variety Algebraic Geometry: Salt Lake City 2015, Proc. Symp. Pure Math., Vol. 97.1, 2018	arxiv
Towards a link theoretic characterization of smoothness (with Y.-C. Tu) Math. Res. Lett. 24 (2017), 1239-1262	journal arxiv
Birational rigidity of singular Fano hypersurfaces Ann. Sc. Norm. Super. Pisa, Cl. Sci. 17 (2017), 911-929	journal 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	journal 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	journal 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

BOOKS EDITED

Algebraic Geometry: Salt Lake City 2015 (T. de Fernex, B. Hassett, M. Mustaţă, M. Olsson, M. Popa, and R. Thomas, eds.) Proc. Symp. Pure Math., Vols. 97.1 and 97.2, 2018
Surveys on Recent Developments in Algebraic Geometry (I. Coskun, T. de Fernex, and A. Gibney, eds.) Proc. Symp. Pure Math., Vol. 95, 2017
Local and global methods in algebraic geometry proceedings for the conference in honor of Lawrence Ein’s 60th birthday, Chicago, 2016 (N. Budur, T. de Fernex, R. Docampo, and K. Tucker, eds.) Contemp. Math., Vol. 712, 2018

OTHER WRITINGS

Vanishing theorems and singularities in birational geometry (with L. Ein and M. Mustata) book in preparation
On rationality of complex algebraic varieties Lectures given for the Ph.D. course On rationality of complex algebraic varieties, University of Rome “Tor Vergata”, May/June 2021.	draft
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