1,697 research outputs found
The set of toric minimal log discrepancies
We describe the set of minimal log discrepancies of toric log varities, and
study its accumulation points.Comment: 11 pages, LaTeX. to appear in Central European Journal of Mathematic
Resonance varieties and Dwyer-Fried invariants
The Dwyer-Fried invariants of a finite cell complex X are the subsets
\Omega^i_r(X) of the Grassmannian of r-planes in H^1(X,\Q) which parametrize
the regular \Z^r-covers of X having finite Betti numbers up to degree i. In
previous work, we showed that each \Omega-invariant is contained in the
complement of a union of Schubert varieties associated to a certain subspace
arrangement in H^1(X,\Q). Here, we identify a class of spaces for which this
inclusion holds as equality. For such "straight" spaces X, all the data
required to compute the \Omega-invariants can be extracted from the resonance
varieties associated to the cohomology ring H^*(X,\Q). In general, though,
translated components in the characteristic varieties affect the answer.Comment: 39 pages; to appear in "Arrangements of Hyperplanes - Sapporo 2009,"
Advanced Studies in Pure Mathematic
Robert MacPherson and arithmetic groups
We survey contributions of Robert MacPherson to the theory of arithmetic
groups. There are two main areas we discuss: (i) explicit reduction theory for
Siegel modular threefolds, and (ii) constructions of compactifications of
locally symmetric spaces. The former is joint work with Mark McConnell, the
latter with Lizhen Ji.Comment: Dedicated to Robert MacPherson on the occasion of his 60th birthda
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