共查询到20条相似文献,搜索用时 31 毫秒
1.
《代数通讯》2013,41(4):1679-1691
Abstract The real Torelli mapping, from the moduli space of real curves of genus g to the moduli space of g-dimensional real principally polarized abelian varieties, sends a real curve into its real Jacobian. The real Schottky problem is to describe its image. The results contained in the present paper concern hyperelliptic real curves and in particular real curves of genus 2. We exhibit also some counterexamples for the non-hyperelliptic case. 相似文献
2.
The image of the complement of a hyperplane arrangement under a monomial map can be tropicalized combinatorially using matroid theory. We apply this to classical moduli spaces that are associated with complex reflection arrangements. Starting from modular curves, we visit the Segre cubic, the Igusa quartic, and moduli of marked del Pezzo surfaces of degrees 2 and 3. Our primary example is the Burkhardt quartic, whose tropicalization is a 3-dimensional fan in 39-dimensional space. This effectuates a synthesis of concrete and abstract approaches to tropical moduli of genus 2 curves. 相似文献
3.
Mika Seppälä 《manuscripta mathematica》1982,40(1):79-86
The moduli space Xg of compact Riemann surfaces of genus g, g>1, has a canonical antiholomorphic involution. It can easily be defined in terms of complex curves: a point in Xg represented by a curve C is mapped to the point represented by the complex conjugate ¯C of C. In other words, the moduli space has a canonical real structure (cf. Andreotti and Holm [2]). The Teichmüller space has, however, several essentially distinct real structures. The purpose of this note is to describe all real structures of the Teichmüller space T(g,n) of compact Riemann surfaces of genus g punctured at n points.Work supported by the EMIL AALTONEN FOUNDATION 相似文献
4.
The orientable cover of the moduli space of real genus zero algebraic curves with marked points is a compact aspherical manifold tiled by associahedra, which resolves the singularities of the space of phylogenetic trees. The resolution maps planar metric trees to their underlying abstract representatives, collapsing and folding an explicit geometric decomposition of the moduli space into cubes, endowing the resolving space with an interesting canonical pseudometric. Indeed, the given map can be reinterpreted as relating the real and the tropical versions of the Deligne–Knudsen–Mumford compactification of the moduli space of Riemann spheres. 相似文献
5.
In this work we study the additive orbifold cohomology of the moduli stack of smooth genus g curves. We show that this problem reduces to investigating the rational cohomology of moduli spaces of cyclic covers of curves where the genus of the covering curve is g. Then we work out the case of genus g = 3. Furthermore, we determine the part of the orbifold cohomology of the Deligne–Mumford compactification of the moduli space of genus 3 curves that comes from the Zariski closure of the inertia stack of ${\mathcal{M}3}$ . 相似文献
6.
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
7.
Michael A. van Opstall 《manuscripta mathematica》2006,119(1):115-127
The stable (in the sense of the relative minimal model program) degenerations of symmetric squares of smooth curves of genus
g>2 are computed. This information is used to prove that the component of the moduli space of stable surfaces parameterizing
such surfaces is isomorphic to the moduli space of stable curves of genus g. 相似文献
8.
Han‐Bom Moon 《Mathematische Nachrichten》2015,288(7):824-836
We complete Mori's program with symmetric divisors for the moduli space of stable six‐pointed rational curves. As an application, we give an alternative proof of the complete Mori's program of the moduli space of genus two stable curves, which was first done by Hassett. 相似文献
9.
Curtis T. McMullen 《Journal of the American Mathematical Society》2003,16(4):857-885
This paper exhibits an infinite collection of algebraic curves isometrically embedded in the moduli space of Riemann surfaces of genus two. These Teichmüller curves lie on Hilbert modular surfaces parameterizing Abelian varieties with real multiplication. Explicit examples, constructed from L-shaped polygons, give billiard tables with optimal dynamical properties.
10.
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
11.
We study moduli spaces of K3 surfaces endowed with a Nikulin involution and their image in the moduli space R g of Prym curves of genus g. We observe a striking analogy with Mukai’s well-known work on ordinary K3 surfaces. Many of Mukai’s results have a very precise Prym-Nikulin analogue, for instance a general Prym curve from R g is a section of a Nikulin surface if and only if g ≤ 7 and g ≠ 6. Furthermore, R 7 has the structure of a fibre space over the corresponding moduli space of polarized Nikulin surfaces. We then use these results to study the geometry of the moduli space of even spin curves, with special emphasis on the transition case of which is a 21-dimensional Calabi-Yau variety. 相似文献
12.
13.
In this paper we give an explicit construction of the moduli space of the pointed complete Gorenstein curves of arithmetic genus g with a given quasi-symmetric Weierstrass semigroup, that is, a Weierstrass semigroup whose last gap is equal to 2g – 2. We identify such a curve with its image under the canonical embedding in the (g – 1)-dimensional projective space. By normalizing the coefficients of the quadratic relations and by constructing Gröbner bases of the canonical ideal, we obtain the equations of the moduli space in terms of Buchberger's criterion. Moreover, by analyzing syzygies of the canonical ideal we establish criteria that make the computations less expensive. 相似文献
14.
15.
I. M. Krichever 《Functional Analysis and Its Applications》2012,46(2):110-120
Using meromorphic differentials with real periods, we prove Arbarello’s conjecture that any compact complex cycle of dimension g - n in the moduli space M g of smooth algebraic curves of genus g must intersect the locus of curves having a Weierstrass point of order at most n. 相似文献
16.
Nicola Pagani 《Advances in Mathematics》2012,229(3):1643-1687
In this work we describe the Chen–Ruan cohomology of the moduli stack of smooth and stable genus 2 curves with marked points. In the first half of the paper we compute the additive structure of the Chen–Ruan cohomology ring for the moduli stack of stable n-pointed genus 2 curves, describing it as a rationally graded vector space. In the second part we give generators for the even Chen–Ruan cohomology ring as an algebra on the ordinary cohomology. 相似文献
17.
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
18.
C. G. Zaal 《Compositio Mathematica》1999,119(2):209-212
We construct in all characteristics p7lt;2 a complete surface in the moduli space of smooth genus 6 curves. The surface is contained in the locus of curves with automorphisms. 相似文献
19.
An orientation reversing involution of a topological compact genus surface induces an antiholomorphic involution of the Teichmüller space of genus g Riemann surfaces. Two such involutions and are conjugate in the mapping class group if and only if the corresponding orientation reversing involutions and of are conjugate in the automorphism group of . This is equivalent to saying that the quotient surfaces and are homeomorphic. Hence the Teichmüller space has distinct antiholomorphic involutions, which are also called real structures of ([7]). This result is a simple fact that follows from Royden's theorem ([4]) stating that the the mapping class group is
the full group of holomorphic automorphisms of the Teichmüller space (). Let and be two real structures that are not conjugate in the mapping class group. In this paper we construct a real analytic diffeomorphism
such that
This mapping d is a product of full and half Dehn–twists around certain simple closed curves on the surface . This has applications to the moduli spaces of real algebraic curves. A compact Riemann surface admitting an antiholomorphic involution is a real algebraic curve of the topological type . All fixed–points of the real structure of the Teichmüller space , are real curves of the above topological type and every real curve of that topological type is represented by an element
of the fixed–point set of . The fixed–point set is the Teichmüller space of real algebraic curves of the corresponding topological type. Given two different real structures
and , let d the the real analytic mapping satisfying (1). It follows that d maps onto and is an explicit real analytic diffeomorphism between these Teichmüller spaces.
Received 8 December 1997; accepted 12 August 1998 相似文献
20.
S. V. Shadrin 《Functional Analysis and Its Applications》2003,37(1):78-80
We express Hurwitz numbers of polynomials of arbitrary topological type in terms of intersection numbers on the moduli space of curves of genus zero with marked points. 相似文献