The DOI matches its Crossref record; 17 of the 17 references it cites were found in a registry or an index.
Moduli spaces of weighted pointed stable curves
Open accessAbstract
Abstract A weighted pointed curve consists of a nodal curve and a sequence of marked smooth points, each assigned a number between zero and one. A subset of the marked points may coincide if the sum of the corresponding weights is no greater than one. We construct moduli spaces for these objects using methods of the log minimal model program, and describe the induced birational morphisms between moduli spaces as the weights are varied. In the genus zero case, we explain the connection to Geometric Invariant Theory quotients of points in the projective line, and to compactifications of moduli spaces studied by Kapranov, Keel, and Losev-Manin.
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Cites
Mumford, D., Fogarty, J., & Kirwan, F. (1994) · Springer Grundlehren · doi:10.1007/978-3-642-57916-5 · Cited by 2,564
The irreducibility of the space of curves of given genus
Deligne, P., & Mumford, D. (1969) · Publications Mathématiques de l'IHÉS · doi:10.1007/bf02684599 · Cited by 1,631
The projectivity of the moduli space of stable curves, II: The stacks $M_{g,n}$
Knudsen, F. F. (1983) · MATHEMATICA SCANDINAVICA · doi:10.7146/math.scand.a-12001 · Cited by 739
(1998) · Graduate Texts in Mathematics · doi:10.1007/b98867 · Cited by 503 · cited 1×
“The divisor κ = u∗[c1(ωu) (2)], where u : Cn → Mn is the universal curve, is ample ([HM] 3.”
BackgroundThe projectivity of the moduli space of stable curves. I: Preliminaries on "det" and "Div".
Knudsen, F., & Mumford, D. (1976) · MATHEMATICA SCANDINAVICA · doi:10.7146/math.scand.a-11642 · Cited by 492
Geometric invariant theory and flips
Thaddeus, M. (1996) · Journal of the American Mathematical Society · doi:10.1090/s0894-0347-96-00204-4 · Cited by 315
Chow quotients of Grassmannians. I
Kapranov, M. (1993) · ADVSOV · doi:10.1090/advsov/016.2/02 · Cited by 308
Variation of geometric invariant theory quotients
Dolgachev, I., & Hu, Y. (1998) · Publications mathématiques de l IHÉS · doi:10.1007/bf02698859 · Cited by 304
Quasi-projective Moduli for Polarized Manifolds
Viehweg, E. (1995) · Springer eBooks · doi:10.1007/978-3-642-79745-3 · Cited by 282
Smooth Compactification of Locally Symmetric Varieties
Ash, A. (1975) · Cited by 265
Metadata
- Authors
- Hassett, B.
- Venue
- Advances in Mathematics
- Publisher
- Elsevier BV
- Published
- 2003-02
- Volume
- 173
- Issue
- 2
- Pages
- 316-352
- ISSN
- 0001-8708 (ISSN-L)
- OpenAlex
- W1978192778
- Cited by
- 289
- References
- 17
- FWCI
- 3.72
- Type
- journal article
- Language
- en
- Open access
- bronze
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