Nero Budur

H.J. Kenna Assistant Professor

B.S., University of Illinois at Chicago, 1998
Ph.D., University of Illinois at Chicago, 2003

Research Interests

My work is in the general area of Algebraic Geometry. This is the study of geometric objects of a somewhat more rigid nature then topological or analytical objects since they are solutions of systems of polynomial equations. My focus is on singularities, which are the peculiar places where these objects are not smooth, and on their effect on the local and global geometry of these shapes.

My interests include thresholds and discrepancies of higher-dimensional birational algebraic geometry, motivic integration, multiplier ideals, D-modules and Hodge theory, local systems and Higgs bundles, geometric stability.

Selected Publications

• On Hodge spectrum and multiplier ideals, Math. Ann. 327, no. 2, 257-270 (2003).
• (with M. Casanellas and E. Gorla) Hilbert functions of integral standard determinantal schemes and integral arithmetically Gorenstein schemes, J. Algebra 272, no. 1, 292-310 (2004).
• (with Morihiko Saito) Multiplier ideals, V-filtration, and spectrum, J. Algebraic Geom. 14 (2005), 269-282.
• On the V-filtration of D-modules, in "Geometric methods in algebra and number theory", F. Bogomolov, Y. Tschinkel (Eds.), Progress in Mathematics 235, Birkhäuser (2005).
• (with Mircea Mustaţă and Morihiko Saito) Roots of Bernstein-Sato polynomials for monomial ideals:  a positive characteristic approach, Math. Res. Lett. 13, no. 1, 125-142 (2006)
• (with Mircea Mustaţă and Morihiko Saito) Bernstein-Sato polynomials of arbitrary varieties, Compositio Math. 142, 779-797 (2006)
• (with Mircea Mustaţă and Morihiko Saito) Combinatorial description of the roots of the Bernstein-Sato polynomials for monomial ideals, to appear in Comm. Algebra.

Please direct questions and comments to: budur.1@nd.edu