共查询到20条相似文献,搜索用时 0 毫秒
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M. L. Kontsevich 《Functional Analysis and Its Applications》1991,25(2):123-129
Institute of Information Transmission Problems, Academy of Sciences of the USSR. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 25, No. 2, pp. 50–57, April–June, 1991. 相似文献
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The Euler characteristic of the moduli space of curves 总被引:1,自引:0,他引:1
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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
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Research partially supported by NSF Grant #DMS-84-02209. 相似文献
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Naoki Murabayashi 《manuscripta mathematica》1994,84(1):125-133
We consider the moduli spaceS
n
of curvesC of genus 2 with the property:C has a “maximal” mapf of degreen to an elliptic curveE. Here, the term “maximal” means that the mapf∶C→E doesn't factor over an unramified cover ofE. By Torelli mapS
n
is viewed as a subset of the moduli spaceA
2 of principally polarized abelian surfaces. On the other hand the Humbert surfaceH
Δ of invariant Δ is defined as a subvariety ofA
2(C), the set of C-valued points ofA
2. The purpose of this paper is to releaseS
n
withH
Δ. 相似文献
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Maryam Mirzakhani 《Journal of the American Mathematical Society》2007,20(1):1-23
In this paper, we establish a relationship between the Weil- Petersson volume of the moduli space of hyperbolic Riemann surfaces with geodesic boundary components of lengths , and the intersection numbers of tautological classes on the moduli space of stable curves. As a result, by using the recursive formula for obtained in the author's Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces, preprint, 2003, we derive a new proof of the Virasoro constraints for a point. This result is equivalent to the Witten-Kontsevich formula.
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《复变函数与椭圆型方程》2013,58(11):1527-1548
We show that under mild boundary conditions the moduli space of non-compact curves on a complex surface is (locally) an analytic subset of a ball in a Banach manifold, defined by finitely many holomorphic functions. 相似文献
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We give a new method for generating genus 2 curves over a finite field with a given number of points on the Jacobian of the curve. We define two new invariants for genus 2 curves as values of modular functions on the Hilbert moduli space and show how to compute them. We relate them to the usual three Igusa invariants on the Siegel moduli space and give an algorithm to construct curves using these new invariants. Our approach simplifies the complex analytic method for computing genus 2 curves for cryptography and reduces the amount of computation required. 相似文献
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We consider the moduli space of pointed non-singular curves of genus g whose Weierstrass gap sequence has the largest gap \(\ell _g\) equal to \(2g-3\). We stratify the moduli space by the sequence of osculating divisors associated to a canonically embedded curve. A monomial basis for the space of higher orders regular differentials on the curves in each stratum is constructed. Numerical conditions are given on the semigroup imposing that one of the strata is empty. Several examples are presented. 相似文献
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By computing the class of the universal antiramification locus of the Gauss map, we obtain a complete birational classification by Kodaira dimension of the universal theta divisor over the moduli space of curves. 相似文献
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Michela Artebani 《Transactions of the American Mathematical Society》2008,360(3):1581-1599
S. Kondo used periods of surfaces to prove that the moduli space of genus three curves is birational to an arithmetic quotient of a complex 6-ball. In this paper we study Heegner divisors in the ball quotient, given by arithmetically defined hyperplane sections of the ball. We show that the corresponding loci of genus three curves are given by hyperelliptic curves, singular plane quartics and plane quartics admitting certain rational ``splitting curves'.
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Shigeyuki Morita 《Topology》2003,42(4):787-819
In this paper, we prove that the tautological algebra in cohomology of the moduli space Mg of smooth projective curves of genus g is generated by the first [g/3] Mumford-Morita-Miller classes. This solves a part of Faber's conjecture (Moduli of Curves and Abelian Varieties Vieweg, Braunschweig, 1999) concerning the structure of the tautological algebra affirmatively. More precisely, for any k we express the kth Mumford-Morita-Miller class ek as an explicit polynomial in the lower classes for all genera g=3k−1,3k−2,…,2. 相似文献
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Gavril Farkas 《Advances in Mathematics》2010,223(2):433-443
We determine the Kodaira dimension of the moduli space Sg of even spin curves for all g. Precisely, we show that Sg is of general type for g>8 and has negative Kodaira dimension for g<8. 相似文献
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