Lucia Caporaso

PAPERS

On a compactification of the Universal Picard Variety over the Moduli Space of Stable Curves. Ph.D. Thesis, Harvard University 1993

A compactification of the Universal Picard Variety over the Moduli Space of Stable Curves. (pdf) Journal of American Mathematics Society, Vol. 7, N. 3, July 94 p. 589-660.

Uniformity of Rational Points. (pdf) With Joe Harris and Barry Mazur - Journal of American Mathematics Society, Vol.10, N.1, Jan.97, p. 1-35.

How many rational points can a curve have? With Joe Harris and Barry Mazur -The Moduli space of curves, Progress in mathematics n. 129, Birkhàuser (1995) p.13-32.

Distribution of Rational points and Kodaira dimension of fiber products. The Moduli space of curves, Progress in mathematics n. 129, Birkhàuser (1995) p.1-12.

Counting rational points on algebraic curves.(dvi) Rend. Sem. Mat. Politecnico dell'Un. di Torino, Vol. 53,3 (1996) Number theory.

Parameter spaces for curves on surfaces and enumeration of rational curves. With Joe Harris - Compositio Mathematica 113, p.155-208 (1998).

Enumeration of rational curves: the rational fibration method. With Joe Harris - Compositio Mathematica 113, p.209-236 (1998).

Counting plane curves of any genus.(dvi) With Joe Harris. Inventiones mathematicae, Vol 131(2), p. 345-392 (1998).

Counting curves on surfaces: a guide to new techniques and results. (dvi) European Congress of Mathematics, Progress in mathematics n. 168, Birkhàuser, p.136-149.

On certain uniformity properties of curves over function fields. (ps) Compositio Mathematica Vol 130 No 1. January 2002

Recovering plane curves from their bitangents. (dvi) With Edoardo Sernesi. Journal of Algebraic Geometry 12 (2003) no. 2, pp. 225-244.

On modular properties of odd theta-characteristics.(dvi) Contemporary Mathematics Vol 276, 2001 (Advances in Algebraic Geometry Motivated by Physics) p.101-114.

Remarks about uniform boundedness of rational points over function fields. (dvi) Transactions of AMS 355, Number 9, pp 3475-3484 (2003)

Characterizing curves by their odd theta-characteristics. (dvi) With Edoardo Sernesi. Journal fur die reine und angewandte Mathematik 562 101-135 (2003)

Combinatorial properties of stable spin curves. (pdf) With Cinzia Casagrande. Communications in Algebra: Special issue in Honor of Professor Steven Kleiman. Vol. 31, N. 8 pp 3653-3672 (2003).

Moduli theory and arithmetic of algebraic varieties. (pdf) Proceedings of the Fano conference. Edited by A. Collino, A. Conte, M. Marchisio pp. 353-379

Moduli of roots of line bundles on curves.(pdf) With Cinzia Casagrande and Maurizio Cornalba. (2004) Transactions of the American Mathematical Society 359 (2007), 3733-3768. On line version .

Neron models and compactified Picard schemes over the moduli stack of stable curves. (pdf) (2005) American Journal of Mathematics, Vol 130 p.1-47, 2008.

On Abel maps of stabe curves. (pdf) (2006) With Eduardo Esteves. Michigan Mathematical Journal, Vol. 55, 575- 607, 2007

Naturality of Abel maps. (pdf) Manuscripta Mathematica Vol. 123, Number 1, May 2007, pages 53-71. On line version .

Geometry of the theta divisor of a compactified jacobian. (pdf) Journal of the European Mathematical Society (2009) 11, 1385 - 1427.

Compactified Jacobians, Abel maps and Theta divisors. (pdf) Curves and Abelian varieties: international conference, in honor of Roy Smith's 65th birthday. March 30-April 2, 2007, University of Georgia, Athens, Georgia Edited by Valery Alexeev, Arnaud Beauville, C. Herbert Clemens, Elham Izadi. Contemporary Mathematics Volume 465. AMS Bookstore, 2008

Abel maps of Gorenstein curves. (pdf) With Eduardo Esteves and Juliana Coelho. Rendiconti del Circolo Matematico di Palermo - Volume 57, Number 1 / April, 2008. pp.33-59

Brill-Noether theory of binary curves. (pdf) To appear in Mathematical Research Letters (18 pages) Math arXiv:0807.1484 (2008).

Linear series on semistable curves. (pdf) Math arXiv:0812.1682 (2008). (34 pages)

Torelli theorem for graphs and tropical curves.(pdf) With Filippo Viviani. To appear in Duke Mathematical Journal (30 pages). Math arXiv:0901.1389 (2009).

Torelli theorem for stable curves. (pdf) With Filippo Viviani. Math arXiv:0904.4039 (2009). (33 pages)

Geometry of tropical moduli spaces and linkage of graphs. (pdf) Math arXiv: (2010). (25 pages)