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Mauricio Velasco Department of Mathematics |
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Research
My research focuses on the interplay between commutative algebra, algebraic geometry and combinatorial topology. I am interested in the minimal free resolutions of monomial ideals and in particular the extent to which their structure can be described by means of CW complexes. I am also very interested in the Cox rings of algebraic varieties, especially the relationship between their combinatorial invariants (Hilbert series, Betti numbers, Grobner fans,...) and the geometry of divisors on the varieties.
I am a Morrey
assistant professor at UC
Berkeley. I graduated from Cornell in 2007 under the
direction of Mike
Stillman.
Articles
Picard graded Betti numbers and
the defining
ideals of Cox rings (with A.Laface). Submitted [.pdf ]
Minimal free resolutions that are not
supported by a CW-complex. [pdf ] Journal
of Algebra Volume 319, Issue 1, 1 January 2008, Pages 102-114
Grobner bases, monomial group actions and the
Cox rings of Del Pezzo surfaces (with M. Stillman and D. Testa).
[pdf ] Journal of Algebra, Volume 316, Issue 2,
15 October 2007, Pages 777-801 Computational Algebra
Frames and Degenerations of Monomial Ideals (with Irena Peeva). Submitted
[pdf ].