Mathias Lederer

Visiting Scholar of Mathematics

Web Site N/A Contact Information Office:  525 Malott Hall Phone:  (607) 255-4008 Fax:  (607) 255-7149 Email:  mlederer@math.cornell.edu

Education

Ph.D. (2005) Leopold-Franzens-University of Innsbruck

Research Area: algebraic geometry

I am interested in Hilb^r, the Hilbert scheme of r points in affine space over an arbitrary ring. This Hilbert scheme contains subschemes Hilb′^δ, for every standard set of size r in the n-fold product of the natural numbers. Hilb′^δ is the moduli space of reduced Groebner bases with standard set delta. The scheme Hilb′^δ contains an open subscheme Hilb′^δ0, the moduli space of objects in Hilb′^δ such that in addition, they define an etale family. I recently proved a counting formula for the irreducible and connected components of the scheme Hilb′^δ0. This formula, conjectured by Bernd Sturmfels, expresses the number of components purely in terms of a combinatorial invariant of delta. Currently I am trying to take this result to the edge: I want to prove that the number of irreducible components of Hilb′^δ1 is given by the same invariant of delta. Here Hilb′^δ1 is the intersection of Hilb′^δ with the good component of Hilb^r.

Selected Publications

The vanishing ideal of a finite set of closed points in affine space, J. Pure Appl. Algebra 212 (2008), 1116–1133.

Finite sets of d-planes in affine space, J. Algebra 321 no. 12 (2009), 3827–3849.

Grobner strata in the Hilbert scheme of points, preprint math.AG/0907.0302v4 (2010), 41 pages.

Components of Grobner strata in the Hilbert scheme of points, preprint math.AG/1006.3653 (2010), 38 pages.

Last modified: July 6, 2010