Geometric Invariant Theory for Polarized Curves

  • Gilberto Bini
  • Fabio Felici
  • Margarida Melo
  • Filippo Viviani
Part of the Lecture Notes in Mathematics book series (LNM, volume 2122)

Table of contents

  1. Front Matter
    Pages i-x
  2. Gilberto Bini, Fabio Felici, Margarida Melo, Filippo Viviani
    Pages 1-16
  3. Gilberto Bini, Fabio Felici, Margarida Melo, Filippo Viviani
    Pages 17-26
  4. Gilberto Bini, Fabio Felici, Margarida Melo, Filippo Viviani
    Pages 27-44
  5. Gilberto Bini, Fabio Felici, Margarida Melo, Filippo Viviani
    Pages 45-59
  6. Gilberto Bini, Fabio Felici, Margarida Melo, Filippo Viviani
    Pages 61-72
  7. Gilberto Bini, Fabio Felici, Margarida Melo, Filippo Viviani
    Pages 73-80
  8. Gilberto Bini, Fabio Felici, Margarida Melo, Filippo Viviani
    Pages 81-90
  9. Gilberto Bini, Fabio Felici, Margarida Melo, Filippo Viviani
    Pages 91-105
  10. Gilberto Bini, Fabio Felici, Margarida Melo, Filippo Viviani
    Pages 107-116
  11. Gilberto Bini, Fabio Felici, Margarida Melo, Filippo Viviani
    Pages 117-130
  12. Gilberto Bini, Fabio Felici, Margarida Melo, Filippo Viviani
    Pages 131-139
  13. Gilberto Bini, Fabio Felici, Margarida Melo, Filippo Viviani
    Pages 141-147
  14. Gilberto Bini, Fabio Felici, Margarida Melo, Filippo Viviani
    Pages 149-154
  15. Gilberto Bini, Fabio Felici, Margarida Melo, Filippo Viviani
    Pages 155-165
  16. Gilberto Bini, Fabio Felici, Margarida Melo, Filippo Viviani
    Pages 167-170
  17. Gilberto Bini, Fabio Felici, Margarida Melo, Filippo Viviani
    Pages 171-195
  18. Gilberto Bini, Fabio Felici, Margarida Melo, Filippo Viviani
    Pages 197-203
  19. Back Matter
    Pages 205-214

About this book

Introduction

We investigate GIT quotients of polarized curves. More specifically, we study the GIT problem for the Hilbert and Chow schemes of curves of degree d and genus g in a projective space of dimension d-g, as d decreases with respect to g. We prove that the first three values of d at which the GIT quotients change are given by d=a(2g-2) where a=2, 3.5, 4. We show that, for a>4, L. Caporaso's results hold true for both Hilbert and Chow semistability. If 3.5<a<4, the Hilbert semistable locus coincides with the Chow semistable locus and it maps to the moduli stack of weakly-pseudo-stable curves. If 2<a<3.5, the Hilbert and Chow semistable loci coincide and they map to the moduli stack of pseudo-stable curves. We also analyze in detail the critical values a=3.5 and a=4, where the Hilbert semistable locus is strictly smaller than the Chow semistable locus. As an application, we obtain three compactications of the universal Jacobian over the moduli space of stable curves, weakly-pseudo-stable curves and pseudo-stable curves, respectively.

Keywords

14L24,14H40,14C05,14H10,14D23,14B05. Compactified Jacobians Geometric invariant theory Hilbert and Chow schemes of curves Stable and (weakly) pseudostable curves Universal Jacobian

Authors and affiliations

  • Gilberto Bini
    • 1
  • Fabio Felici
    • 2
  • Margarida Melo
    • 3
  • Filippo Viviani
    • 4
  1. 1.Dipartimento di Matematica "F. Enriques"Università degli Studi di MilanoMilanoItaly
  2. 2.Dipartimento di Matematica e FisicaUniversità degli Studi di Roma TreRomeItaly
  3. 3.Departamento de MatemáticaUniversidade de CoimbraCoimbraPortugal
  4. 4.Dipartimento di Matematica e FisicaUniversità degli Studi di Roma TreRomeItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-11337-1
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-11336-4
  • Online ISBN 978-3-319-11337-1
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book