Tommaso de Fernex

Associate Professor, Warnock Chair

Research: My research interests are in algebraic geometry. The main focus is on problems in birational geometry of higher dimensional varieties, minimal model program, and singularity theory.

• Curriculum vitae: html (short), pdf (long)
• Past and future talks

Preprints and Publications:

• Rigidity properties of Fano varieties (with C. Hacon). Submitted.

• On the Mori cone of blow-ups of the plane. Submitted.

• Shokurov's ACC Conjecture for log canonical thresholds on smooth varieties (with L. Ein and M. Mustata). To appear in Duke Math. J. arxiv

• Deformations of canonical pairs and Fano varieties (with C. Hacon). To appear in J. reine angew. Math. arxiv

• A vanishing theorem for log canonical pairs (with L. Ein). To appear in Amer. J. Math. arxiv

• Singularities on normal varieties (with C. Hacon). Compositio Math. 145 (2009), 393-414. arxiv

• Limits of log canonical thresholds (with M. Mustata). Ann. Sci. École Norm. Sup. 42 (2009), 493-517. 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. Res. Inst. Math. Sci. 44 (2008), 425-448. Special issue dedicated to Professor H. Hironaka. 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. 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.