Maurizio Cornalba - mathematical publications

Papers

M. Cornalba, B. Shiffman, A counterexample to the transcendental Bezout problem, Ann. of Math. 96 (1972), 402-406.

M. Cornalba, Two theorems on modifications of analytic spaces, Invent. Math. 20 (1973), 227-247.

M. Cornalba, P. Griffiths, Analytic cycles and vector bundles on non-compact algebraic varieties, Invent. Math. 28 (1975), 1-106.

M. Cornalba, P. Griffiths, Some transcendental aspects of algebraic geometry, in "Algebraic Geometry, Arcata 1974", Proceedings of Symposia in Pure Mathematics 29, A.M.S., Providence, Rhode Island, 1975, 3-110.

M. Cornalba, F. D'Amone, G. Gheri, F. Pegoraro, Su di una tecnica ibrida per la risoluzione numerica del flusso di Morozov con funzioni speciali, Consiglio Tecnico Scientifico della Difesa, C.A.M.E.N. (Centro Applicazioni Militari Energia Nucleare), internal report 1062, March 1975.

M. Cornalba, Complex tori and Jacobians, in "Complex Analysis and its Applications", vol. 2, I.A.E.A., Vienna, 1976, 39-100.

E. Arbarello, M. Cornalba, Su una proprietà notevole dei morfismi di una curva a moduli generali in uno spazio proiettivo, Rend. Sem. Mat. Univers. Politecn. Torino 38 (1980), 87-99.

E. Arbarello, M. Cornalba, La congettura di Petri nel caso delle curve piane, in "Geometria Algebraica y Algebra", H. Tapia-Recillas, editor, C.I.E.A. del I.P.N., México, 1980, 4-9.

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

E. Arbarello, M. Cornalba, Footnotes to a paper of Beniamino Segre, Math. Ann. 256 (1981), 341-362.

M. Cornalba, Una osservazione sulla topologia dei rivestimenti ciclici di varietà algebriche, Boll. UMI (5) 18-A (1981), 323-328.

R. Catenacci, M. Cornalba, C. Reina, On the energy spectrum and parameter spaces of classical CPn models, Comm. Math. Phys. 89 (1983), 375-386.

E. Arbarello, M. Cornalba, A few remarks about the variety of irreducible plane curves of given degree and genus, Ann. Sci. Éc. Norm. Sup. (4) 16 (1983), 467-488.

R. Catenacci, M. Cornalba, C. Reina, Classical solutions of CPn non-linear models: an algebraic-geometric description, Journal of Geometry and Physics 1 (1984), 53-84.

M. Cornalba, Il nuovo volto della teoria delle curve algebriche, Boll. UMI (6) 3-A (1984), 335-351.

M. Cornalba, Systèmes pluricanoniques sur l'espace des modules des courbes et diviseurs de courbes k-gonales (d'après Harris et Mumford), Séminaire Bourbaki, 36e année (1983-1984), Exposé 615, Astérisque 121-122 (1985), 7-24.

F. Brezzi, M. Cornalba, A. Di Carlo, How to get around a simple quadratic fold, Numer. Math. 48 (1986), 417-427.

R. Catenacci, M. Cornalba, M. Martellini, C. Reina, Algebraic Geometry and Path Integrals for Closed Strings, Physics Letters B 172 (1986), 328-332.

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

M. Cornalba, The bosonic string from an algebro-geometric standpoint, in "Superstrings, Unified Theories, and Cosmology", G. Furlan, R. Jengo, J.C. Pati et al., editors, World Scientific, Singapore, 1987, 38-52.

M. Cornalba, On the locus of curves with automorphisms, Annali di Matematica pura ed applicata (4) 149 (1987), 135-151. Erratum, Annali di Matematica pura ed applicata (4) 187 (2008), 185-186. Revised version incorporating the changes described in the Erratum.

M. Cornalba, Il luogo singolare dello spazio dei moduli delle curve, Rend. Sem. Mat. Fis. Milano 57 (1987), 149-159.

M. Cornalba, J. Harris, Divisor classes associated to families of stable varieties, with applications to the moduli space of curves, Ann. Sci. Éc. Norm. Sup. (4) 21 (1988), 455-475.

M. Cornalba, The theorems of Riemann-Roch and Abel, in "Lectures on Riemann Surfaces", M. Cornalba, X. Gomez-Mont, A. Verjovsky, editors, World Scientific, Singapore, 1989, 302-349.

M. Cornalba, Moduli of curves and theta-characteristics, in "Lectures on Riemann Surfaces", M. Cornalba, X. Gomez-Mont, A. Verjovsky, editors, World Scientific, Singapore, 1989, 560-589.

M. Cornalba, A remark on the Picard group of spin moduli space, Rend. Mat. Acc. Lincei (9) 2 (1991), 211-217.

M. Cornalba, On the projectivity of the moduli spaces of curves, J. reine angew. Math. 443 (1993), 11-20.

M. Cornalba, A simple proof of the projectivity of Kontsevich's space of maps, Istit. Lombardo Accad. Sci. Lett. Rend. A 129 (1995), 97-105.

E. Arbarello, M. Cornalba, Combinatorial and algebro-geometric cohomology classes on the moduli spaces of curves, J. Alg. Geom. 5 (1996), 705-749, arXiv:alg-geom/9406008.

M. Cornalba, Cohomology of moduli spaces of stable curves, Proceedings of the International Congress of Mathematicians (Berlin, 1998), Doc. Math., Extra volume ICM 1998, II (1998), 249 - 257. (slides of ICM98 talk)

E. Arbarello, M. Cornalba, Calculating cohomology groups of moduli spaces of curves via algebraic geometry, Inst. Hautes Études Sci. Publ. Math. 88 (1998), 97-127, arXiv:math/9803001.

M. Cornalba, Coomologia in grado basso degli spazi di moduli delle curve, in "F. Brioschi (1824-1897). Convegno di studi matematici", Istituto Lombardo, Milano, 1999, 303-312.

M. Cornalba, Compattificazioni di spazi di moduli di radici di fibrati in rette, in "L. Cremona (1830-1903). Convegno di studi matematici", Istituto Lombardo, Milano, 2005, 119-131.

M. Cornalba, The Picard group of the moduli stack of stable hyperelliptic curves, Rend. Lincei Mat. Appl. (9) 18 (2007), 109-115, arXiv:math/0605531.

L. Caporaso, C. Casagrande, M. Cornalba, Moduli of roots of line bundles on curves, Trans. Amer. Math. Soc. 359 (2007), 3733-3768, arXiv:math/0404078.

M. Cornalba, L. Stoppino, A sharp bound for the slope of double cover fibrations, Michigan Math. J. 56 (2008), 551-561, arXiv:math/0510144.

E. Arbarello, M. Cornalba, Teichmüller space via Kuranishi families, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 8 (2009), 89-116, arXiv:math/0702437.

E. Arbarello, M. Cornalba, Jenkins-Strebel differentials, Rend. Lincei Mat. Appl. (9) 21 (2010), 115-157.

E. Arbarello, M. Cornalba, Divisors in the moduli spaces of curves, in "Geometry of Riemann surfaces and their moduli spaces" (Lizhen Ji, Scott Wolpert, Shing-Tung Yau, editors), Surveys in Differential Geometry 14, International Press, Somerville, MA, 2010, pp. 1-22. arXiv:0810.5373.

M. Cornalba, L'eredità scientifica di Guido Castelnuovo a 150 anni dalla nascita, Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 149 (2015), 45-55.

Books

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. Reprinted in "Phillip A. Griffiths, Selected Works of Phillip A. Griffiths with Commentary, volume II, American Mathematical Society, Providence, RI, 2003, pp. 649-778".

E. Arbarello, M. Cornalba, P. Griffiths, J. Harris, Geometry of Algebraic Curves, vol. I. Grundlehren der mathematischen Wissenschaften 267. Springer-Verlag, New York, 1985.

E. Arbarello, M. Cornalba, P. Griffiths, Geometry of Algebraic Curves, vol. II, with a contribution by J. Harris. Grundlehren der mathematischen Wissenschaften 268. Springer-Verlag, Heidelberg, 2011.

Books edited

Lectures on Riemann Surfaces (M. Cornalba, X. Gomez-Mont, A. Verjovsky, editors), World Scientific, Singapore, 1989.

Problems in the theory of surfaces and their classification (F. Catanese, C. Ciliberto, M. Cornalba, editors), Symposia Mathematica 32, Academic Press, London, 1991. 

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.