Enrico Arbarello - Scientific Publication


Papers

E. Arbarello,Weierstrass points and moduli of curves, Compositio Mathematica 29 (1974), 325-342.

E. Arbarello, Alcune osservazioni sui moduli delle curve appartenenti a una data superficie algebrica, Lincei-Rend. Sc. fis. mat. e nat. 59 (1975) 725-732.

E. Arbarello, E. Sernesi, Petri's approach to the study of the ideal associated to a special divisor, Inventiones math. 49 (1978), 99-119.

E. Arbarello, On subvarieties of the moduli space of curves of genus g defined in terms of Weierstrass points, Lincei-Memorie Sc. fisiche, ecc. 15  (1978), 1-20.

E. Arbarello, M. Cornalba, La congettura di Petri nel caso delle curve piane, Centro de Investigacion y de Estudios Avanzados del IPN, Mexico, (1979).

E. Arbarello,  E. Sernesi, The equation of a plane curve, Duke Math. J. 49 (1979), 469-485.

E. Arbarello, M. Cornalba, Su una congettura di K. Petri, Comment. Math. Helvetici 56 (1981), 1-38.

E. Arbarello,M. Cornalba, Su di una proprieta' notevole dei morfismi di una curva a moduli generali in uno spazio proiettivo, Rend. Sem. Mat. Univers. Politecn. Torino 38 (1980).

E. Arbarello, J. Harris, Canonical curves and quadrics of rank 4, Compositio Mathematica 43 (1981), 145-179.

E. Arbarello, M. Cornalba, Footnotes to a paper of B. Segre: the number of g  's on a general d-gonal curve and the unirationality of the Hurwitz space of 4-gonal and 5-gonal curves, Math. Ann. 256 (1981), 341-362.

E. Arbarello, C. Ciliberto, Petri's adjoint ideal, Commutative Algebra, Prceedings of the Trento Conference, Marcel Dekker 1983.

E. Arbarello, M. Cornalba, A few remarks about the variety of irreducible plane curves of given degree and genus, Ann. scient. Ec. Norm. Sup. 16 (1983), 467-488.

E. Arbarello, M. Cornalba, P. Griffiths, J. Harris, Special divisors on algebraic curves, Informal lecture notes distributed in conjunction with the principal lectures at the Regional Algebraic Geometry Conference, Athens, Georgia, May 7-May 12, 1979.

E. Arbarello, C. De Concini, On a set of equations  characterizing Riemann matrices, Annals of Math. 120 (1984), 119-140.

E. Arbarello,  C. De Concini, An analytical translation of a criterion of Welters  and its relation with the K.P. hierarchy, Algebraic Geometry Sitges 1983, Lectures Notes in Math. 1124, Springer-Verlag, New York, 1985, 1-20.

E. Arbarello,  Periods of Abelian Integrals, Theta Functions, and Differential Equations of KdV Type, Proceedings of the International Congress of Mathematicians, Berkeley 1986, 623-628.

E. Arbarello, M. Cornalba, The Picard groups of the moduli space of curves, Topology 26 (1987), 153-171.

E. Arbarello, Fay's Trisecant Formula and a Characterization of Jacobian Varieties, Proceedings of Symposia in Pure Mathematics, 46 (1987), 49-61.

E. Arbarello,   C. De Concini, Another proof of a conjecture of S.P. Novikov on Periods of Abelian Integrals on Riemann Surfaces, Duke Math. J. 54, a special volume in honor of Yuri Ivanovich Manin (1987), 163-178.

E. Arbarello, C. De Concini, V.G. Kac,e C. Procesi, Moduli Spaces of Curves and Representation Theory, Commun. Math. Phys. 117 (1988), 1-36.

E. Arbarello, Superficie di Riemann, funzioni theta e teoria della rappresentazione, Bollettino U.M.I. 7 (1989),1-22.

E. Arbarello, C. De Concini, V.G. Kac, The infinite wedge representation and the reciprocity law for algebraic curves, Proceedings of Symposia in Pure Mathematics 49 (1989), 171-190.

E. Arbarello, C. De Concini, Geometrical aspects of the Kadomtsev-Petviashvili equation, in "Global Geometry and mathematical Physics", SLN 1451, 95-137. 1991.

E. Arbarello, C. De Concini, Abelian varieties, infinite dimensional Lie Algebras and the heat equation, Proceedings of Symposia in Pure Mathematics, 53 (1991), 1-31.

E. Arbarello, Aspetti geometrici delle equazioni di tipo KdV.  Enciclopedia del XX Secolo, Treccani;

E. Arbarello, M. Cornalba, Combinatorial and Algebro-Geometric cohomology classes on the Moduli Spaces of  Curves , J. Algebraic Geometry, 5 (1996), 705-709. (combalgcls.pdf)

E. Arbarello,  M. Cornalba, Calculating cohomology groups of moduli spaces of curves via algebraic geometry,  Publ. Math. I.H.E.S. 88 (1998), 97-127.  (coho.mg.pdf) (coho.mg.ps)

E. Arbarello, Introduction to Kontsevich's result on Deformation-Quantization ofPoisson Structures, in Seminari di geometria Algebrica, Scuola Normale
Superiore, (1999), 5-20.

E. Arbarello,  Survey of Work on the Schottky Problem up to 1996, in  "The Red Book of Varieties and Schemes" by David Mumford, second expanded edition
Springer, p.286-291. (1999)

E. Arbarello,  Sketches of KdV,  Contemporary Math.Volume 312, (2002),  p. 9-69. (Skt.KdV.pdf)(Skt.KdV.ps)

E. Arbarello,   Geometria Numerativa, Invarianti di Gromov-Witten e moduli delle curve algebriche, Storia della Scienza,
Vol IX, Enciclopedia Treccani, (2003), 1-23.

E. Arbarello, I. Krichever, G. Marini,  Characterizing Jacobians via flexes of the Kummer variety, Math. Research Letters  Vol. 13, Issue 1 (2006),  109-123.

E. Arbarello, Moduli spaces of curves. Five lectures. In: 26th Brazilian Mathematics Colloquium, Instituto Nacional de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, Brazil,  (2007).

E. Arbarello, Superfici di Riemann,  in La matematica, Problemi e Teoremi, Volume secondo,  Giulio Einaudi Editore, Torino,  vol. 21; p. 115-157. (2008)

E. Arbarello, M. Cornalba, Teichmüller space via Kuranishi families,  in Ann. Sc. Norm. Super. Pisa Cl. Sci. vol. VIII; p. 89-116. (2009)

E. Arbarello, M. Cornalba, Divisors in the moduli spaces of  In: Lizhen Ji, Scott Wolpert, Shing-Tung Yau, Editors
Surveys in Differential Geometry Volume 14 Geometry of Riemann surfaces and their moduli spaces. vol. 14, p. 1-22, Sommerville, MA: International Press. (2009)

E. Arbarello, M. Cornalba, Jenkins-Strebel differentials. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 21, no. 2, 115–157. (2010)

E. Arbarello, G. Mondello, Two remarks on the Weierstrass flag. Compact moduli spaces and vector bundles, 137–144, Contemp. Math., 564, Amer. Math. Soc., Providence, RI, (2012).

E. Arbarello, G. Saccà, A. Ferretti,  Relative Prym varieties associated to the double cover of an Enriques surface, (arXiv:1211.4268) , (2012),
To appear in the Journal of Differential Geometry (2014) p. 1-60.

E.Arbarello, A. Bruno, E. Sernesi, Mukai's program for curves on a K3 surface, (arXiv:1309.0496) , (2013). To appear in Algebraic Geometry (2014)

Books

E. Arbarello, M. Cornalba, P. Griffiths, J. Harris, The Geometry of Algebraic Curves, Volume I, Grundlehren der mathematischen Wissenschaften, Vol 267, Springer-Verlag 1985, Berlin, Heidelberg, New York. ISBN 978-1-4419-2825-2

E. Arbarello, M. Cornalba, P. Griffiths, with a contribution by Joseph Daniel  Harris, The Geometry of Algebraic Curves, Volume II, Grundlehren der mathematischen Wissenschaften, Vol 268, Springer-Verlag, 2011, Berlin, Heidelberg, New York,
XXX, 963 p. DOI: 10.1007/978-3-540-69392-5

Books edited

Guido Castelnuovo, Opere Matematiche. Memorie e Note (E. Arbarello, U. Bottazzini, M. Cornalba, P. Gario, E. Vesentini, editors), vol. 1: 1885-1893, Accademia Nazionale dei Lincei, Roma, 2002; vol. 2: 1894-1906, Accademia Nazionale dei Lincei, Roma, 2003; vol. 3: 1907-1930, Accademia Nazionale dei Lincei, Roma, 2004; vol. 4: 1931-1952; Appendice, Accademia Nazionale dei Lincei, Roma, 2007.

Phillip A. Griffiths, Selected Works of Phillip A. Griffiths with Commentary (Enrico Arbarello, Robert L. Bryant, C. Herbert Clemens, Maurizio Cornalba, Mark L. Green, Joe Harris, David R. Morrison, and Wilfried Schmid, editors), 4 volumes, American Mathematical Society, Providence, RI, 2003.

In Preparation

E. Arbarello, G. Saccà,  Remarks on Lazarsfeld-Mukai bundles and quiver varieties.