 

Tyler J. Jarvis
The Picard Group of the Moduli of Higher Spin Curves


Published: 
May 10, 2001 
Keywords: 
Picard group, moduli, higher spin curves, Witten conjecture. 
Subject: 
14H10, 32G15; 81T40, 14N, 14M 


Abstract
This article treats the Picard group of the
moduli (stack) of rspin curves and its compactification.
Generalized spin curves, or rspin curves are a natural
generalization of 2spin curves (algebraic curves with a
thetacharacteristic), and have been of interest lately because they
are the subject of a remarkable conjecture of E. Witten, and because
of the similarities between the intersection theory of these moduli
spaces and that of the moduli of stable maps.
We generalize results of Cornalba, describing and giving relations
between many of the elements of the Picard group of the stacks.
These relations are important in the proof of the genuszero case of
Witten's conjecture given in [14]. We use these relations to
show that when 2 or 3 divides r, the Picard group has nonzero
torsion. And finally, we work out some specific examples.


Acknowledgements
This material is based on work supported in part by the National Science Foundation under Grant No. DMS9501617 and by the National Security Agency under Grant No. MDA9049910039


Author information
Department of Mathematics, Brigham Young University, Provo, UT 84602
jarvis@math.byu.edu
http://www.math.byu.edu/~jarvis/

