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Dan Abramovich
Professor of Mathematics
- CONTACT INFO
Office: 118 Kassar-Gould House
Phone: (401) 863-7968
Fax: (401) 863-9013
Email: abrmovic<at>math.brown.edu
Mailing Address:
Mathematics Department
Box 1917
Brown University
Providence, RI 02912
- COURSE SCHEDULE
Spring 2006
- RESEARCH INTERESTS
Algebraic and Arithmetic Geometry
- BACKGROUND
Education: Ph.D., Harvard University, 1991.
- RECENT PUBLICATIONS
Algebraic orbifold quantum products. Orbifolds in mathematics and physics (Madison, WI, 2001), 1--24, Contemp. Math., 310, Amer. Math. Soc., Providence, RI, 2002. (w/ Graber, Tom; Vistoli, Angelo)
Moduli of twisted spin curves. Proc. Amer. Math. Soc. 131 (2003), no. 3, 685--699 (electronic). (w/ Jarvis, Tyler J.)
Torification and factorization of birational maps. J. Amer. Math. Soc. 15 (2002), no. 3, 531--572 (electronic). (w/ Karu, Kalle; Matsuki, Kenji; W\l odarczyk, Jaros\l aw)
Uniformity of stably integral points on principally polarized abelian varieties of dimension $\le2$. Israel J. Math. 121 (2001), 351--380. (w/ Matsuki, Kenji)
Compactifying the space of stable maps. J. Amer. Math. Soc. 15 (2002), no. 1, 27--75 (electronic). (w/ Vistoli, Angelo)
Complete moduli for fibered surfaces. Recent progress in intersection theory (Bologna, 1997), 1--31, Trends Math., Birkhäuser Boston, Boston, MA, 2000. (w/ Vistoli, Angelo)
The formula $12=10+2\times 1$ and its generalizations: counting rational curves on $\bold F\sb 2$. Advances in algebraic geometry motivated by physics (Lowell, MA, 2000), 83--88, Contemp. Math., 276, Amer. Math. Soc., Providence, RI, 2001. (w/ Bertram, Aaron)
Stable maps and Hurwitz schemes in mixed characteristics. Advances in algebraic geometry motivated by physics (Lowell, MA, 2000), 89--100, Contemp. Math., 276, Amer. Math. Soc., Providence, RI, 2001. (w/ Oort, Frans)
Correction:"A note on the factorization theorem of toric birational maps after Morelli and its toroidal extension" Tohoku Math. J. (2) 51 (1999), no. 4, 489--537; (w/ Matsuki, Kenji)
Alterations and resolution of singularities. Resolution of singularities (Obergurgl, 1997), 39--108, Progr. Math., 181, Birkhäuser, Basel, 2000. (w/ Oort, Frans)
Weak semistable reduction in characteristic 0. Invent. Math. 139 (2000), no. 2, 241--273. (w/ Karu, K.)
A note on the factorization theorem of toric birational maps after Morelli and its toroidal extension. Tohoku Math. J. (2) 51 (1999), no. 4, 489--537. (w/ Matsuki, Kenji; Rashid, Suliman)
Smoothness, semistability, and toroidal geometry. J. Algebraic Geom. 6 (1997), no. 4, 789--801. (w/ de Jong, A. J.)
Lang maps and Harris's conjecture. Israel J. Math. 101 (1997), 85--91.
A high fibered power of a family of varieties of general type dominates a variety of general type. Invent. Math. 128 (1997), no. 3, 481--494.
Uniformity of stably integral points on elliptic curves. Invent. Math. 127 (1997), no. 2, 307--317.
Equivariant resolution of singularities in characteristic $0$. Math. Res. Lett. 4 (1997), no. 2-3, 427--433. (w/ Wang, Jianhua)
A linear lower bound on the gonality of modular curves. Internat. Math. Res. Notices 1996, no. 20, 1005--1011.
Lang's conjectures, fibered powers, and uniformity. New York J. Math. 2 (1996), 20--34, electronic. (w/ Voloch, JoséFelipe)/I>
Uniformité des points rationnels des courbes alébriques sur les extensions quadratiques et cubiques. (French) [Uniformity of rational points of algebraic curves over quadratic and cubic extensions] C. R. Acad. Sci. Paris Sér. I Math. 321 (1995), no. 6, 755--758
Formal finiteness and the torsion conjecture on elliptic curves. A footnote to a paper: "Rational torsion of prime order in elliptic curves over number fields" [Astérisque No. 22 (1995), 3, 81--10] by S. Kamienny and B. Mazur. Columbia University Number Theory Seminar (New York, 1992). Astérisque No. 228 (1995), 3, 5--17.
Subvarieties of semiabelian varieties. Compositio Math. 90 (1994), no. 1, 37--52.
Toward a proof of the Mordell-Lang conjecture in characteristic $p$. Internat. Math. Res. Notices 1992, no. 5, 103--115.(w/ Voloch, José Felipe
Lectures on Arakelov geometry. With the collaboration of D. Abramovich, J.-F. Burnol and J. Kramer. Cambridge Studies in Advanced Mathematics, 33. Cambridge University Press, Cambridge, 1992. viii+177 pp. ISBN: 0-521-41669-8 (Soulé, C).
Abelian varieties and curves in $W\sb d(C)$. Compositio Math. 78 (1991), no. 2, 227--238. (w/ Harris, Joe)