Abstract
The aim of this chapter is to collect the definitions and basic properties of the curves that we will deal with throughout the manuscript.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
J. Alper, Adequate moduli spaces and geometrically reductive group schemes. Algebr. Geom. Preprint available at arXiv:1005.2398 (to appear)
J. Alper, D.I. Smyth, F. van der Wyck, Weakly proper moduli stacks of curves. Preprint available at arXiv:1012.0538
E. Arbarello, M. Cornalba, P.A. Griffiths, Geometry of Algebraic Curves. Volume II. With a contribution by Joseph Daniel Harris. Grundlehren der Mathematischen Wissenschaften, vol. 268 (Springer, Heidelberg, 2011)
L. Caporaso, A compactification of the universal Picard variety over the moduli space of stable curves. J. Am. Math. Soc. 7, 589–660 (1994)
F. Catanese, Pluricanonical-Gorenstein-curves, in Enumerative Geometry and Classical Algebraic Geometry (Nice, 1981). Progress in Mathematics, vol. 24 (Birkhäuser Boston, Boston, 1982), pp. 51–95
P. Deligne, D. Mumford, The irreducibility of the space of curves of given genus. Inst. Hautes Études Sci. Publ. Math. 36, 75–109 (1969)
D. Edidin, Notes on the construction of the moduli space of curves, in Recent Progress in Intersection Theory (Bologna, 1997). Trends in Mathematics (Birkh auser Boston, Boston, 2000), pp. 85–113
D. Gieseker, Lectures on Moduli of Curves. Tata Institute of Fundamental Research Lectures on Mathematics and Physics, vol. 69 (Tata Institute of Fundamental Research, Bombay, 1982)
J. Hall, Moduli of singular curves. Preprint (2010). Available at arXiv:1011.6007v1
B. Hassett, D. Hyeon, Log canonical models for the moduli space of curves: first divisorial contraction. Trans. Am. Math. Soc. 361, 4471–4489 (2009)
D. Hyeon, Y. Lee, Stability of tri-canonical curves of genus two. Math. Ann. 337, 479–488 (2007)
D. Hyeon, I. Morrison, Stability of tails and 4-canonical models. Math. Res. Lett. 17(4), 721–729 (2010)
F.F. Knudsen, The projectivity of the moduli space of stable curves. II. The stacks M g, n . Math. Scand. 52(2), 161–199 (1983)
M. Melo, Compactified Picard stacks over the moduli stack of stable curves with marked points. Adv. Math. 226, 727–763 (2011)
D. Mumford, Stability of projective varieties. Enseignement Math. (2) 23, 39–110 (1977)
D. Schubert, A new compactification of the moduli space of curves. Compositio Math. 78, 297–313 (1991)
E. Sernesi, Deformations of Algebraic Schemes. Grundlehren der mathematischen Wissenschaften, vol. 334 (Springer, New York, 2006)
D.I. Smyth, Towards a classification of modular compactifications of M g, n . Invent. Math. 192, 459–503 (2013)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Bini, G., Felici, F., Melo, M., Viviani, F. (2014). Singular Curves. In: Geometric Invariant Theory for Polarized Curves. Lecture Notes in Mathematics, vol 2122. Springer, Cham. https://doi.org/10.1007/978-3-319-11337-1_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-11337-1_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-11336-4
Online ISBN: 978-3-319-11337-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)