TOMMASO de FERNEX
Assistant Professor
Warnock Chair

University of Utah
Dept. of Mathematics
155 South 1400 East
Salt Lake City, UT 84112

Office: JWB 322
Phone: (801) 581-7121
Fax: (801) 581-6851

defernex@math.utah.edu

Tommaso de Fernex

Assistant Professor, Warnock Chair

 

Teaching - Fall 2008:

Research: My research interests are in algebraic geometry, and primarily focus on problems in birational geometry of higher dimensional varieties and singularity theory.

Preprints and Publications:

  • A vanishing theorem for log canonical pairs (with L. Ein). Submitted. arxiv

  • Singularities on normal varieties (with C. Hacon). Submitted. arxiv

  • Limits of log canonical thresholds (with M. Mustata). Accepted for publication in Ann. Sci. Ecole Norm. Sup. arxiv

  • Ample subvarieties and rationally connected fibrations (with M. Beltrametti and A. Lanteri). Math. Ann. 341 (2008), 897-926. arxiv

  • Divisorial valuations via arcs (with L. Ein and S. Ishii). Publ. RIMS 44 (2008), 425-448. Special issue dedicated to Professor Heisuke Hironaka on the occasion of his ``Kiju", that is, his 77th birthday. 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. arxiv

  • Multiplicities and log canonical threshold (with L. Ein and M. Mustata). J. Algebraic Geom. 13 (2004), 603-615. 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

  • On planar Cremona maps of prime order. Nagoya Math. J. 174 (2004), 1-28. 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.

  • Ample vector bundles and intrinsic quadric fibrations over irrational curves. Matematiche (Catania) 55 (2000), 205-222.

  • 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:

  • Applications of vanishing theorems and multiplier ideals (with L. Ein and M. Mustata). Monograph in preparation.

  • 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. In preparation.

  • Birational maps of varieties. Ph.D. Thesis, University of Illinois at Chicago, June 2002.

  • Birational transformations of prime order of the projective plane. Tesi di Dottorato, Università di Genova, February 2001.

  • Fibrati vettoriali ampi con sezioni nulle su fibrazioni in coniche. Tesi di Laurea, Università di Milano, February 1996.

Research partially supported by the National Science Foundation.