CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCJM
Abstract view

Author's Draft

Smoothing of Limit Linear Series of Rank One on Saturated Metrized Complexes of Algebraic Curves

  • Ye Luo,
    School of Information Science and Engineering, Xiamen University
  • Madhusudan Manjunath,
    Department of Mathematics, Indian Institute of Technology, Bombay
Format:   LaTeX   MathJax   PDF  

Abstract

We investigate the smoothing problem of limit linear series of rank one on an enrichment of the notions of nodal curves and metrized complexes called saturated metrized complexes. We give a finitely verifiable full criterion for smoothability of a limit linear series of rank one on saturated metrized complexes, characterize the space of all such smoothings, and extend the criterion to metrized complexes. As applications, we prove that all limit linear series of rank one are smoothable on saturated metrized complexes corresponding to curves of compact-type, and prove an analogue for saturated metrized complexes of a theorem of Harris and Mumford on the characterization of nodal curves contained in a given gonality stratum. In addition, we give a full combinatorial criterion for smoothable limit linear series of rank one on saturated metrized complexes corresponding to nodal curves whose dual graphs are made of separate loops.
Keywords: limit linear series, metrized complex limit linear series, metrized complex
MSC Classifications: 14T05 show english descriptions Tropical geometry [See also 12K10, 14M25, 14N10, 52B20] 14T05 - Tropical geometry [See also 12K10, 14M25, 14N10, 52B20]
 

© Canadian Mathematical Society, 2017 : https://cms.math.ca/