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Mauricio Velasco Department of Mathematics |
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Research
My research area is the common ground between commutative algebra, combinatorics and algebraic geometry. My current main interests are the Cox rings of algebraic varieties, especially the relationship between their algebraic invariants and the geometry of the varieties. I am also interested in the geometry of the Hilbert schemes of points. Some of my previous work focused on free resolutions of monomial ideals and their connections with combinatorial topology.
Currently I am a
Morrey
assistant professor at UC
Berkeley. I graduated from Cornell in 2007 under the
direction of Mike
Stillman.
Articles
Cox rings of degree one Del Pezzo surfaces (with D. Testa and A. Varilly-Alvarado). To appear in Algebra and Number Theory [ArXiv ]
Hilbert Schemes of eight points (with D. Cartwright, D. Erman and B. Viray). To appear in Algebra and Number Theory [ArXiv ]
Picard graded Betti numbers and the defining ideals of Cox rings (with A.Laface). [ArXiv ]. To appear in J. of Algebra.
A survey on Cox rings (with A.Laface). [.pdf ]
Geometriae Dedicata: Volume 139, Issue 1 (2009)
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
Big rational surfaces (with D. Testa and A. Varilly-Alvarado). Submitted [ArXiv]
Koszul obstructions for deformations of punctual schemes of regularity two (with D. Erman). Submitted [ArXiv ]
Blow-ups of P^{n-3} at n points and Spinor varieties (with B. Sturmfels). Submitted [ArXiv
]
Frames and Degenerations of Monomial Ideals (with I. Peeva). [pdf ]
To appear in TAMS.