Publications

  • T. de Fernex and R. Docampo (2020). Differentials on the arc space. Duke Math. J. Vol. 169, 353-396. Published, 01/2020.
  • T. de Fernex and R. Docampo (2019). Nash blow-ups of jet schemes. Ann. Inst. Fourier. Vol. 69, 2577-2588. Published, 12/2019.
  • N. Budur, T. de Fernex, R. Docampo, and K. Tucker (2018). Local and global methods in algebraic geometry, proceedings for the conference in honor of Lawrence Ein’s 60th birthday, Chicago, 2016. Vol. 712. Contemp. Math. Published, 12/2018.
  • T. de Fernex, B. Hassett, M. Mustata, M. Olsson, M. Popa, and R. Thomas (2018). Algebraic Geometry: Salt Lake City 2015. Vol. 97. Proc. Symp. Pure Math. Published, 12/2018.
  • T. de Fernex (2018). The arc space of an algebraic variety. Algebraic Geometry: Salt Lake City 2015, Proc. Symp. Pure Math. Vol. 97. Published, 12/2018.
  • T. de Fernex, L. Ein and S. Ishii (2018). Jet closures and the local isomorphism problem. J. Algebra. Vol. 501, 166-181. Published, 12/2018.
  • I. Coskun, T. de Fernex, and A. Gibney (2017). Surveys on Recent Developments in Algebraic Geometry. Vol. 95. Proc. Symp. Pure Math. Published, 12/2017.
  • T. de Fernex (2017). Birational geometry of singular Fano hypersurfaces. Ann. Sc. Norm. Super. Pisa. Vol. 17, 911-929. Published, 12/2017.
  • T. de Fernex and Y.-C. Tu (2017). Towards a link theoretic characterization of smoothness. Math. Res. Lett. Vol. 24, 1239-1262. Published, 12/2017.
  • T. de Fernex (2017). Colength of a product of ideals, in appendix to: J. Kollar and A. Nemethi, Dufree’s conjecture on the signature of smoothings of surface singularities. (pp. 787-798). Vol. 50. Ann. Sci. E ́cole Norm. Sup. Published, 12/2017.
  • T. de Fernex (2016). Erratum to: Birationally rigid hypersurfaces(Invent Math, (2013), 192, (533-566), Doi:10.1007/s00222-012-0417-0). Inventiones Mathematicae. Vol. 203, 675-680. Published, 02/01/2016.
  • T. de Fernex and R. Docampo (2016). Terminal valuations and the Nash problem. Inventiones Mathematicae. Vol. 203, 303-331. Published, 01/01/2016.
  • T. de Fernex and M. Mustata, The volume of a set of arcs on a variety, Rev. Roumaine Math. Pures Appl. 60 (2015), 375–401, special issue in honor of Lucian Badescu’s 70th birthday. Published, 12/2015.
  • T. de Fernex and M. Mustata (2015). The volume of a set of arcs on a variety. Rev. Roumaine Math. Pures Appl. Vol. 60, 375-401. Published, 12/2015.
  • S. Boucksom, T. de Fernex, C. Favre and S. Urbinati (2015). Valuation spaces and multiplier ideals on singular varieties. “Recent Advances in Algebraic Geometry,” a volume in honor of Rob Lazarsfeld’s 60th birthday, London Math. Soc. Lecture Note Series, Cambridge University Press. 29-51. Published, 12/2015.
  • S. Boucksom, T. de Fernex, C. Favre and S. Urbinati (2015). Valuation spaces and multiplier ideals on singular varieties. Recent Advances in Algebraic Geometry: A Volume in Honor of Rob Lazarsfeld's 60th Birthday. 29-51. Published, 01/01/2015.
  • T. de Fernex, R. Docampo, S. Takagi and K. Tucker (2015). Comparing multiplier ideals to test ideals on numerically Q-Gorenstein varieties. Bulletin of the London Mathematical Society. Vol. 47, 359-369. Published, 01/01/2015.
  • T. de Fernex (2014). Fano hypersurfaces and their birational geometry. Springer Proceedings in Mathematics and Statistics. Vol. 79, 103-120. Published, 01/01/2014.
  • T. de Fernex and R. Docampo (2014). Jacobian discrepancies and rational singularities. Journal of the European Mathematical Society. Vol. 16, 165-199. Published, 01/01/2014.
  • T. de Fernex (2013). Three-dimensional counter-examples to the Nash problem. Compositio Mathematica. Vol. 149, 1519-1534. Published, 09/01/2013.
  • T. de Fernex (2013). Birationally rigid hypersurfaces. Inventiones Mathematicae. Vol. 192, 533-566. Published, 06/01/2013.
  • T. de Fernex and D. Fusi (2013). Rationality in families of threefolds. Rendiconti del Circolo Matematico di Palermo. Vol. 62, 127-135. Published, 04/01/2013.
  • S. Boucksom, T. de Fernex and C. Favre (2012). The volume of an isolated singularity. Duke Mathematical Journal. Vol. 161, 1455-1520. Published, 07/31/2012.
  • T. de Fernex and C. Hacon (2011). Rigidity properties of Fano varieties. Current Developments in Algebraic Geometry, MSRI Publications. Vol. 59. Published, 12/2011.
  • T. de Fernex, L. Ein and M. Mustata (2011). Log canonical thresholds on varieties with bounded singularities. Classification of algebraic varieties, EMS Ser. Congr. Rep., Eur. Math. Soc., Zurich. 221–257. Published, 12/2011.
  • T. de Fernex and C. Hacon (2011). Deformations of canonical pairs and Fano varieties. Journal fur die Reine und Angewandte Mathematik. 97-126. Published, 02/01/2011.
  • T. de Fernex and L. Ein (2010). A vanishing theorem for log canonical pairs. American Journal of Mathematics. Vol. 132, 1205-1221. Published, 10/01/2010.
  • T. de Fernex, L. Ein and M. Mustata (2010). Shokurov's ACC conjecture for log canonical thresholds on smooth varieties. Duke Mathematical Journal. Vol. 152, 93-114. Published, 03/01/2010.
  • T. de Fernex and M. Mustata (2009). Limits of log canonical thresholds. Annales Scientifiques de l'Ecole Normale Superieure. Vol. 42, 491-515. Published, 05/01/2009.
  • T. de Fernex and C. Hacon (2009). Singularities on normal varieties. Compositio Mathematica. Vol. 145, 393-414. Published, 03/01/2009.
  • M. Beltrametti, T. de Fernex and A. Lanteri (2008). Ample subvarieties and rationally connected fibrations. Mathematische Annalen. Vol. 341, 897-926. Published, 08/01/2008.
  • T. de Fernex, L. Ein and S. Ishii (2008). Divisorial valuations via arcs. Publications of the Research Institute for Mathematical Sciences. Vol. 44, 425-448. Published, 05/01/2008.
  • T. de Fernex, A. Kuronya and R. Lazarsfeld (2007). Higher cohomology of divisors on a projective variety. Mathematische Annalen. Vol. 337, 443-455. Published, 02/01/2007.
  • T. de Fernex, E. Lupercio, T. Nevins and B. Uribe (2007). Stringy Chern classes of singular varieties. Advances in Mathematics. Vol. 208, 597-621. Published, 01/30/2007.
  • T. de Fernex, E. Lupercio, T. Nevins and B. Uribe (2006). A localization principle for orbifold theories. “Recent Developments in Algebraic Topology,” Proceedings for the Conference in honor of the 70th birthday of S. Gitler, Contemp. Math., Amer. Math. Soc., Providence, RI. Vol. 407, 113-133. Published, 12/2006.
  • T. de Fernex (2006). Length, multiplicity, and multiplier ideals. Transactions of the American Mathematical Society. Vol. 358, 3717-3731. Published, 08/01/2006.
  • T. de Fernex and A. Lanteri (2006). Bad loci of free linear systems. Advances in Geometry. Vol. 6, 93-107. Published, 01/26/2006.
  • T. de Fernex, L. Ein and M. Mustata (2004). Multiplicities and log canonical threshold. Journal of Algebraic Geometry. Vol. 13, 603-615. Published, 07/01/2004.
  • T. de Fernex (2004). On planar Cremona maps of prime order. Nagoya Mathematical Journal. Vol. 174, 1-28. Published, 06/01/2004.
  • T. de Fernex, L. Ein and M. Mustata (2003). Bounds for log canonical thresholds with applications to birational rigidity. Mathematical Research Letters. Vol. 10, 219-236. Published, 03/01/2003.
  • T. de Fernex and L. Ein (2002). Resolution of indeterminacy of pairs. Algebraic Geometry, a Volume in Memory of Paolo Francia, de Gruyter, Berlin. 165–177. Published, 12/2002.
  • T. de Fernex (2001). Trasformazioni birazionali di ordine primo del piano proiettivo. (pp. 435-438). Vol. 4. Bollettino della Unione Matematica Italiana A. Published, 12/01/2001.
  • T. de Fernex, Ample vector bundles and intrinsic quadric fibrations over irrational curves, Matematiche (Catania), 55 (2000), 205–222. Published, 12/2000.
  • T. de Fernex and A. Lanteri, Ample vector bundles and del Pezzo manifolds. Kodai Math. J. 22 (1999), 85–100. Published, 12/1999.
  • T. de Fernex, Ample vector bundles with sections vanishing along conic fibrations over curves, Collect. Math. 49 (1998), 67–79. Published, 12/1998.

Grants, Contracts & Research Gifts

  • The Boot Camp for the 2015 Algebraic Geometry Summer Research Institute (1500652). PI: Angela C Gibney. Co-PI(s): TOMMASO DE-FERNEX. National Science Foundation, 2015 - 01/31/2016. Total project budget to date: $49,900.00
  • Arcs, Valuations, and Multiplier Ideals on Algebraic Varieties (1402907). PI: Tommaso de Fernex. Co-PI(s): TOMMASO DE-FERNEX. National Science Foundation, 2014 - 08/31/2017. Total project budget to date: $130,999.00
  • RTG: Algebraic Geometry and Topology at the University of Utah (1246989). PI: Kenneth W Bromberg. Co-PI(s): TOMMASO DE-FERNEX. National Science Foundation, 2013 - 05/31/2018. Total project budget to date: $2,431,178.00
  • FRG: Collaborative research: Birational geometry and singularities in zero and positive characteristic (1265285). PI: Tommaso de Fernex. Co-PI(s): TOMMASO DE-FERNEX. National Science Foundation, 2013 - 06/30/2016. Total project budget to date: $410,568.00
  • CAREER: Singularities in the Minimal Model Program and Birational Geometry (0847059). PI: de Fernex, Tommaso. Co-PI(s): TOMMASO DE-FERNEX. National Science Foundation, 2009 - 06/30/2015. Total project budget to date: $400,001.00
  • Topological Invariants and Singularities in Birational Geometry (0548325). PI: deFernex, Tommaso. Co-PI(s): TOMMASO DE-FERNEX. National Science Foundation, 2005 - 06/30/2008. Total project budget to date: $86,035.00

Geographical Regions of Interest

  • Western Europe