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Torsion-Free Sheaves and Moduli of Generalized Spin Curves

Published online by Cambridge University Press:  04 December 2007

T. J. JARVIS
T. J. JARVIS
Affiliation:
Department of Mathematics, Brigham Young University, Provo, UT 84602, U.S.A.; e-mail: jarvis@math.byu.edu
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Abstract

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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.

Keywords

spin curvescompactificationmodulitheta-characteristics.
Type
Research Article
Information
Compositio Mathematica , Volume 110 , Issue 3 , February 1998 , pp. 291 - 333
Copyright
© 1998 Kluwer Academic Publishers