Pointed Castelnuovo numbers
Abstract
The classical Castelnuovo numbers count linear series of minimal degree and fixed dimension on a general curve, in the case when this number is finite. For pencils, that is, linear series of dimension one, the Castelnuovo numbers specialize to the better known Catalan numbers. Using the FultonPragacz determinantal formula for flag bundles and combinatorial manipulations, we obtain a compact formula for the number of linear series on a general curve having prescribed ramification at an arbitrary point, in the case when the expected number of such linear series is finite. The formula is then used to solve some enumerative problems on moduli spaces of curves.
 Publication:

arXiv eprints
 Pub Date:
 January 2015
 DOI:
 10.48550/arXiv.1501.04882
 arXiv:
 arXiv:1501.04882
 Bibcode:
 2015arXiv150104882F
 Keywords:

 Mathematics  Algebraic Geometry
 EPrint:
 10 pages. Final version, to appear in Mathematical Research Letters