The supermoduli of SUSY curves with Ramond punctures

  1. Ruipérez, Daniel Hernández
  2. Bruzzo, Ugo
  1. 1 SISSA (Scuola Internazionale Superiore di Studi Avanzati), Via Bonomea 265, 34136, Trieste, Italia
  2. 2 Departamento de Matemática, Universidad Federal da Paraíba, Campus I, João Pessoa, PB, Brazil
  3. 3 INFN Sezione di Trieste
    info

    INFN Sezione di Trieste

    Trieste, Italia

    ROR https://ror.org/05j3snm48

  4. 4 IGAP (Institute for Geometry and Physics), Trieste, Italy
  5. 5 Arnold-Regge Center for Algebra, Geometry and Theoretical Physics, Torino, Italy
  6. 6 Departamento de Matemáticas and IUFFYM (Instituto Universitario de Física Fundamental y Matemáticas), Universidad de Salamanca, Plaza de la Merced 1-4, 37008, Salamanca, Spain
  7. 7 Real Academia de Ciencias Exactas, Físicas y Naturales, Madrid, Spain
Mostrar afiliaciones +
Revista:
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas

ISSN: 1578-7303,  1579-1505

Año de publicación: 2021

Volumen: 115

Número: 3

Tipo: Artículo

DOI: 10.1007/S13398-021-01078-4 GOOGLE SCHOLAR

Otras publicaciones en: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas

Resumen

We construct local and global moduli spaces of supersymmetric curves with Ramond-Ramond punctures. We assume that the underlying ordinary algebraic curves have a level n structure and build these supermoduli spaces as algebraic superspaces, i.e., quotients of étale equivalence relations between superschemes.

Referencias bibliográficas

  • Artin, M.: Algebraic spaces, Yale University Press, New Haven, Conn., 1971. A James K. Whittemore Lecture in Mathematics given at Yale University, 1969, Yale Mathematical Monographs, 3
  • Baranov, M.A., Schwarz, A.S.: On the multiloop contribution to the string theory. Int. J. Modern Phys. A 2, 1773–1796 (1987)
  • Bartocci, C., Bruzzo, U., Hernández Ruipérez, D.: The geometry of supermanifolds, vol. 71 of Mathematics and its Applications, Kluwer Academic Publishers Group, Dordrecht (1991)
  • Berezin, F.A., Leĭtes, D.A.: Supermanifolds. Dokl. Akad. Nauk SSSR 224, 505–508 (1975)
  • Codogni, G., Viviani, F.: Moduli and periods of supersymmetric curves. arXiv:1706.04910v4 [math.AG]
  • Crane, L., Rabin, J.M.: Super Riemann surfaces: uniformization and Teichmüller theory. Commun. Math. Phys. 113, 601–623 (1988)
  • Deligne, P.: Letter to Y.I. Manin. https://publications.ias.edu/sites/default/files/lettre-a-manin-1987-09-25.pdf (1987)
  • Diroff, D.J.: On the super Mumford form in the presence of Ramond and Neveu-Schwarz punctures. J. Geom. Phys. 144, 273–293 (2019)
  • Domínguez Pérez, J.A., Hernández Ruipérez, D., Sancho de Salas, C.: Supersymmetric products of SUSY-curves, in Differential geometric methods in theoretical physics (Rapallo, 1990), vol. 375 of Lecture Notes in Phys., Springer, Berlin, pp. 271–285 (1991)
  • Domínguez Pérez, J.A., Hernández Ruipérez, D., Sancho de Salas, C.: The variety of positive superdivisors of a supercurve (supervortices). J. Geom. Phys. 12, 183–203 (1993)
  • Domínguez Pérez, J.A., Hernández Ruipérez, D., Sancho de Salas, C.: Global structures for the moduli of (punctured) super Riemann surfaces. J. Geom. Phys. 21, 199–217 (1997)
  • Donagi, R., Witten, E.: Super Atiyah classes and obstructions to splitting of supermoduli space. Pure Appl. Math. Q. 9, 739–788 (2013)
  • Donagi, R., Witten, E.: Supermoduli space is not projected In: String-Math 2012, vol. 90 of Proc. Sympos. Pure Math. Am. Math. Soc., Providence, RI, pp. 19–71 (2015)
  • Falqui, G., Reina, C.: A note on the global structure of supermoduli spaces. Commun. Math. Phys. 128, 247–261 (1990)
  • Felder, G., Kazhdan, D., Polishchuk, A.: Regularity of the superstring supermeasure and the superperiod map. arXiv:1905.12805v1 [math.AG], (2019)
  • Friedan, D.: Notes on string theory and two-dimensional conformal field theory. In: Workshop on unified string theories (Santa Barbara, Calif., 1985), World Sci. Publishing, Singapore, pp. 162–213 (1986)
  • Grothendieck, A.: Technique de descente et théorèmes d’existence en géométrie algébrique. V. Les schémas de Picard: théorèmes d’existence. In: Séminaire Bourbaki, Vol. 7, Soc. Math. France, Paris, pp. Exp. No. 232, 143–161 (1995)
  • Hartshorne, R.: Algebraic geometry, Graduate Texts in Mathematics, vol. 52. Springer-Verlag, New York (1977)
  • Keel, S., Mori, S.: Quotients by groupoids. Ann. Math. (2) 145, 193–213 (1997)
  • Knutson, D.: Algebraic spaces, Lecture Notes in Mathematics, Vol. 203, Springer-Verlag, Berlin (1971)
  • Kostant, B.: Graded manifolds, graded Lie theory, and prequantization. In: Differential geometrical methods in mathematical physics (Proc. Sympos., Univ. Bonn, Bonn, 1975), Springer, Berlin, pp. 177–306. Lecture Notes in Math., Vol. 570 (1977)
  • LeBrun, C., Rothstein, M.: Moduli of super Riemann surfaces. Commun. Math. Phys. 117, 159–176 (1988)
  • Manin, Y.I.: Critical dimensions of string theories and a dualizing sheaf on the moduli space of (super) curves. Funktsional. Anal. i Prilozhen. 20, 88–89 (1986)
  • Manin, Y.I.: Quantum strings and algebraic curves. In: Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986), Providence, RI, Amer. Math. Soc., pp. 1286–1295 (1987)
  • Manin, Y.I.: Gauge field theory and complex geometry, vol. 289 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer-Verlag, Berlin, 1988. Translated from the Russian by N. Koblitz and J. R. King, second edition 1997, with an appendix by S. Merkulov
  • Manin, Y.I.: Neveu-Schwarz sheaves and differential equations for Mumford superforms. J. Geom. Phys. 5, 161–181 (1988)
  • Moĭšezon, B.G.: An algebraic analogue of compact complex spaces with a sufficiently large field of meromorphic functions. I. Izv. Akad. Nauk SSSR Ser. Mat. 33, 174–238 (1969)
  • Moĭšezon, B.G.: An algebraic analogue of compact complex spaces with a sufficiently large field of meromorphic functions. II. Izv. Akad. Nauk SSSR Ser. Mat. 33,(1969)
  • Moĭšezon, B.G.: An algebraic analogue of compact complex spaces with a sufficiently large field of meromorphic functions. III. Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 33, 506–548 (1969)
  • Ott, N., Voronov, A.: The supermoduli space of genus zero super Riemann surfaces with Ramond punctures. arXiv:1910.05655 [math.AG]
  • Polyakov, A.M.: Quantum geometry of bosonic strings. Phys. Lett. B 103, 207–210 (1981)
  • Salam, A., Strathdee, J.: Super-gauge transformations. Nuclear Phys. B 76, 477–482 (1974)
  • Sernesi, E.: Deformations of algebraic schemes, vol. 334 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer-Verlag, Berlin (2006)
  • Vaĭntrob, A.Y.: Deformations of complex superspaces and of the coherent sheaves on them. In: Current problems in mathematics. Newest results, Vol. 32, Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1988, pp. 125–211. J. Soviet Math. 51 (1990), no. 1, 2140–2188
  • Witten, E.: Notes on super Riemann surfaces and their moduli. Pure Appl. Math. Q. 15, 57–211 (2019)
  • Zariski, O.: On the purity of the branch locus of algebraic functions. Proc. Nat. Acad. Sci. USA 44, 791–796 (1958)