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    Buryak, Alexandr and Guéré, Jérémy 2016. Towards a description of the double ramification hierarchy for Witten's r-spin class. Journal de Mathématiques Pures et Appliquées,


    Esteves, Eduardo and Pacini, Marco 2016. Semistable modifications of families of curves and compactified Jacobians. Arkiv för Matematik, Vol. 54, Issue. 1, p. 55.


    Pernigotti, Letizia and Verra, Alessandro 2016. On the Rationality of the Moduli of Higher Spin Curves in Low Genus. International Mathematics Research Notices, Vol. 2016, Issue. 13, p. 3856.


    Ballico, Edoardo 2015. Components with the expected codimension in the moduli scheme of stable spin curves. Annales UMCS, Mathematica, Vol. 69, Issue. 1, p. 1.


    Chang, Huai-Liang Li, Jun and Li, Wei-Ping 2015. Witten’s top Chern class via cosection localization. Inventiones mathematicae, Vol. 200, Issue. 3, p. 1015.


    Fan, Huijun Jarvis, Tyler and Ruan, Yongbin 2013. The Witten equation, mirror symmetry, and quantum singularity theory. Annals of Mathematics, Vol. 178, Issue. 1, p. 1.


    Fan, Huijun Jarvis, Tyler J. and Ruan, Yongbin 2008. Geometry and analysis of spin equations. Communications on Pure and Applied Mathematics, Vol. 61, Issue. 6, p. 745.


    Jarvis, Tyler J. Kimura, Takashi and Vaintrob, Arkady 2005. Spin Gromov-Witten Invariants. Communications in Mathematical Physics, Vol. 259, Issue. 3, p. 511.


    SCHORK, MATTHIAS 2005. SOME ALGEBRAICAL, COMBINATORIAL AND ANALYTICAL PROPERTIES OF PARAGRASSMANN VARIABLES. International Journal of Modern Physics A, Vol. 20, Issue. 20n21, p. 4797.


    JARVIS, TYLER J. 2000. GEOMETRY OF THE MODULI OF HIGHER SPIN CURVES. International Journal of Mathematics, Vol. 11, Issue. 05, p. 637.


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Torsion-Free Sheaves and Moduli of Generalized Spin Curves

  • T. J. JARVIS (a1)
  • DOI: http://dx.doi.org/10.1023/A:1000209527158
  • Published online: 01 February 1998
Abstract

This article treats compactifications of the space of generalized spin curves. Generalized spin curves, or r-spin curves, are pairs (X,L) with X a smooth curve and L a line bundle whose rth tensor power is isomorphic to the canonical bundle of X. These are a natural generalization of 2-spin curves (algebraic curves with a theta-characteristic), which have been of interest recently, in part because of their applications to fermionic string theory. Three different compactifications over Z[1/r], all using torsion-free sheaves, are constructed. All three yield algebraic stacks, one of which is shown to have Gorenstein singularities that can be described explicitly, and one of which is smooth. All three compactifications generalize constructions of Deligne and Cornalba done for the case when r=2.

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Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
  • URL: /core/journals/compositio-mathematica
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