共查询到20条相似文献,搜索用时 0 毫秒
1.
Brendan Hassett 《Advances in Mathematics》2003,173(2):316-352
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. 相似文献
2.
Brad Safnuk 《Differential Geometry and its Applications》2009,27(2):179-187
We introduce a new method of calculating intersections on , using localization of equivariant cohomology. As an application, we give a proof of Mirzakhani's recursion relation for calculating intersections of mixed ψ and κ1 classes. 相似文献
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Shuguang Wang 《Geometriae Dedicata》1995,57(2):207-215
We classify, in terms of simple algebraic equations, the fixed point sets of the moduli space of stable bundles over genus 2 curves with anti-holomorphic involutions.Research supported by SRF of University of Missouri. 相似文献
5.
Claudio Fontanari 《Archiv der Mathematik》2007,89(6):530-535
We prove that the orbifold desingularization of the moduli space of stable maps of genus g = 1 recently constructed by Vakil and Zinger has vanishing rational cohomology groups in odd degree k < 11.
Received: 29 January 2007 相似文献
6.
We deal with the covers of degree 4 naturally associated to a bielliptic curve of genus g≥6, giving a proof of the unirationality of the moduli space ?
g
be
of such curves, of the rationality of the Hurwitz scheme ℌ
be
4,
g
of bielliptic curves of even genus g, whereas, when g is odd, we construct a finite map ℂ2
g
-2→?
g
be
and compute its degree.
Received: March 25, 2000; in final form: March 10, 2001?Published online: May 29, 2002 相似文献
7.
We explicitly describe complete, one-dimensional subvarieties of the moduli space of smooth complex curves of genus 3.Supported by the Netherlands Organization for Scientific Research (N.W.O.). 相似文献
8.
In this paper we use admissible covers to investigate the gonality of a stable curve C over . If C is irreducible, we compare its gonality to that of its normalization. If C is reducible, we compare its gonality to that of its irreducible components. In both cases we obtain lower and upper bounds. Furthermore, we show that four admissible covers constructed give rise to generically injective maps between Hurwitz schemes. We show that the closures of the images of three of these maps are components of the boundary of the target Hurwitz schemes, and the closure of the image of the remaining map is a component of a certain codimension‐1 subscheme of the boundary of the target Hurwitz scheme. 相似文献
9.
Tyler J. Jarvis 《Mathematische Zeitschrift》2000,235(1):123-149
This article provides two different, but closely related, moduli problems, which in characteristic zero provide a type of
compactification of the universal Picard over the moduli of stable curves. Although neither is of finite type, both are limits
of a sequence of stacks, each of which is a separated algebraic stack of finite type. We discuss relations to previous compactifications
and partial compactifications, give a number of examples related to this compactification, and work out the structure of its
fibres over certain fixed curves. Some applications are also discussed.
Received January 5, 1998; in final form April 1, 1999 / Published online July 3, 2000 相似文献
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Some real moduli spaces can be presented as real hyperbolic space modulo a non-arithmetic group. The whole moduli space is
made from some incommensurable arithmetic pieces, in the spirit of the construction of Gromov and Piatetski-Shapiro. 相似文献
12.
Özgür Ceyhan 《Advances in Mathematics》2009,221(6):1964-1978
The moduli space of weighted pointed stable curves of genus zero is stratified according to the degeneration types of such curves. We show that the homology groups of are generated by the strata of and give all additive relations between them. We also observe that the Chow groups and the homology groups are isomorphic. This generalizes Kontsevich-Manin's and Losev-Manin's theorems to arbitrary weight data A. 相似文献
13.
Andreas Leopold Knutsen 《Indagationes Mathematicae》2008,19(2):217-238
We give restrictions on the existence of families of curves on smooth projective surfaces S of nonnegative Kodaira dimension all having constant geometric genus pg ? 2 and hyperelliptic normalizations. In particular, we prove a Reider-like result that relies on deformation theory and bending-and-breaking of rational curves in Sym2(S). We also give examples of families of such curves. 相似文献
14.
Motivated by several recent results on the geometry of the modulispaces of stable curves of genus g with n marked points, we determine the birational structureof these spaces for small values of g and n by exploiting suitableplane models of a general curve. More precisely, g,n is shownto be rational for g = 2 and 1 n 12, g = 3 and 1 n 14, g= 4 and 1 n 15, and g = 5 and 1 n 12 相似文献
15.
Indranil Biswas 《Journal of Pure and Applied Algebra》2008,212(10):2298-2306
We study certain moduli spaces of stable vector bundles of rank 2 on cubic and quartic threefolds. In many cases under consideration, it turns out that the moduli space is complete and irreducible and a general member has vanishing intermediate cohomology. In one case, all except one component of the moduli space has such vector bundles. 相似文献
16.
Paul Larsen 《Geometriae Dedicata》2013,162(1):305-323
We study the Cox ring of the moduli space of stable pointed rational curves, ${\overline{M}_{0,n}}$ , via the closely related permutohedral (or Losev-Manin) spaces ${\overline{L}_{n-2}}$ . Our main result establishes $\left(\begin{array}{ll} n \\ 2 \end{array}\right)$ polynomial subrings of ${{\rm Cox}(\overline{M}_{0,n})}$ , thus giving collections of boundary variables that intersect the ideal of relations of ${{\rm Cox}(\overline{M}_{0,n})}$ trivially. As applications, we give a combinatorial way to partially solve the Riemann-Roch problem for ${\overline{M}_{0,n}}$ , and we show that all relations in degrees of ${{\rm Cox}(\overline{M}_{0,6})}$ arising from certain pull-backs from projective spaces are generated by the Plücker relations. 相似文献
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We notice that the Maroni invariant of a trigonal Gorenstein curve of arithmetic genus g larger than four may be equal to zero, and we show that this happens if and only if the g31 admits a non-removable base point, which is necessarily a singularity of the curve. We realize and study trigonal curves on rational scrolls, which in the case, where the g31 admits a base point Q, degenerate to a cone with vertex Q. 相似文献
20.
Ford≥3g and 1≤s≤[g/2], we study the strataN
d, g(s) of degreed genusg spaces curvesC whose normal bundleN
C is stable with stability degree (integer of Lange-Narasimhan) σ(N
C)=2s. We prove thatN
d, g(s) has an irreducible component of the right dimension whose general curve has a normal bundle with the right number of maximal
subbundles. We consider also the semi-stable case (s=0), obtaining similar results. We prove our results by studying the normal bundles of reducible curves and their deformations.
Both authors were partially supported by MIUR and GNSAGA of INdAM (Italy). 相似文献