共查询到20条相似文献,搜索用时 15 毫秒
1.
We prove that the moduli space X(1,7) of (1,7)–polarized abelian surfaces with canonical level–structure is birational to the Fano 3–fold V22 of polar hexagons of the Klein quartic (7). In particular X(1,7) is rational and the birational map to ℙ3 is defined over ℚ. As a byproduct we obtain explicitely the equations of the (1,7)–very–ample–polarized abelian surfaces embedded in ℙ6. 相似文献
2.
We study moduli spaces of abelian varieties in positive characteristic, more specifically the moduli space of principally
polarized abelian varieties on the one hand, and the analogous space with Iwahori type level structure, on the other hand.
We investigate the Ekedahl–Oort stratification on the former, the Kottwitz–Rapoport stratification on the latter, and their
relationship. In this way, we obtain structural results about the supersingular locus in the case of Iwahori level structure,
for instance a formula for its dimension in case g is even. 相似文献
3.
Takeshi Kajiwara 《Archiv der Mathematik》2006,86(1):43-49
We show fundamental properties on embedding of abelian surfaces into projective toric 4-folds, and study the case of the toric
Del Pezzo 4-fold from the viewpoint of the moduli space of abelian surfaces with polarization of type (1, 5).
Received: 31 January 2005; revised: 15 April 2005 相似文献
4.
Tomasz Szemberg 《Mathematische Nachrichten》1997,185(1):239-260
In the present paper we study Kummer surfaces in IP6 arising as projections of a certain family of principally polarized abelian surfaces in IP6. This family was introduced by Adler and van Moerbeke in connection with some Hamiltonian dynamical systems. In this paper we give explicit equations of the associated Kummer surfaces. This enables us to deacribe their moduli space and to give the full list of degenerations. 相似文献
5.
R. Silhol 《Mathematische Zeitschrift》2001,236(4):841-881
6.
In this paper, we shall study the structure of walls for Bridgeland’s stability conditions on abelian surfaces. In particular, we shall study the structure of walls for the moduli spaces of rank 1 complexes on an abelian surface with the Picard number 1. 相似文献
7.
8.
Naoki Murabayashi 《Mathematische Annalen》2008,342(3):657-671
It is known that in the moduli space of elliptic curves, there exist precisely nine -rational points represented by an elliptic curve with complex multiplication by the maximal order of an imaginary quadratic
field. In Murabayashi and Umegaki (J Algebra 235:267–274, 2001) and Umegaki [Determination of all -rational CM-points in the moduli spaces of polarized abelian surfaces, Analytic number theory (Beijng/Kyoto, 1999). Dev.
Math., vol 6. Kluwer, Dordrecht, pp 349–357, 2002] we determined all -rational points in (the moduli space of d-polarized abelian surfaces) represented by a d-polarized abelian surface whose endomorphism ring is isomorphic to the maximal order of a quartic CM-field by using the result
in Murabayashi (J Reine Angew Math 470:1–26, 1996). In this paper, we prove that polarized abelian surfaces corresponding
to these -rational CM points have a -rational model by constructing certain Hecke characters. 相似文献
9.
This paper follows on from Nguyen (Geom Funct Anal 20(1):192–228, 2010), in which we study flat surfaces with erasing forest, these surfaces are obtained by deforming the metric structure of translation surfaces, and their moduli space can be viewed as a deformation of the moduli space of translation surfaces. We showed that the moduli spaces of such surfaces are complex orbifolds, and admit a natural volume form μ Tr. The aim of this paper is to show that the volume of those moduli spaces with respect to μ Tr, normalized by some energy function involving the area and the total length of the erasing forest, is finite. Note that translation surfaces and flat surfaces of genus zero can be viewed as special cases of flat surfaces with erasing forest, and on their moduli space, the volume form μ Tr equals the usual ones up to a multiplicative constant. Using this result we obtain new proofs for some classical results due to Masur-Veech, and Thurston concerning the finiteness of the volume of the moduli space of translation sufaces, and of the moduli space of polyhedral flat surfaces. 相似文献
10.
We show that if 𝒜 is an abelian category satisfying certain mild conditions, then one can introduce the concept of a moduli space of (semi)stable objects which has the structure of a projective algebraic variety. This idea is applied to several important abelian categories in representation theory, like highest weight categories. 相似文献
11.
Kōta Yoshioka 《Compositio Mathematica》2003,138(3):261-288
In this paper, we consider the preservation of stability by using the notion of twisted stability. As applications, (1) we show that moduli spaces of stable sheaves on K3 and abelian surfaces are irreducible and (2) we compute Hodge polynomials of some moduli spaces of stable sheaves on Enriques surfaces. 相似文献
12.
We study the locus of intermediate Jacobians of cubic threefolds within the moduli space of complex principally polarized abelian fivefolds, and its generalization to arbitrary genus—the locus of abelian varieties with a singular odd two-torsion point on the theta divisor. Assuming that this locus has expected codimension g (which we show to be true for g≤5, and conjecturally for any g), we compute the class of this locus, and of its closure in the perfect cone toroidal compactification , in the Chow, homology, and the tautological ring. 相似文献
13.
Victor Rotger 《Transactions of the American Mathematical Society》2004,356(4):1535-1550
In this note we consider several maps that occur naturally between modular Shimura varieties, Hilbert-Blumenthal varieties and the moduli spaces of polarized abelian varieties when forgetting certain endomorphism structures. We prove that, up to birational equivalences, these forgetful maps coincide with the natural projection by suitable abelian groups of Atkin-Lehner involutions.
14.
Shelly Garion 《代数通讯》2013,41(5):2126-2155
In this article we give the asymptotic growth of the number of connected components of the moduli space of surfaces of general type corresponding to certain families of Beauville surfaces with group either PSL(2, p), or an alternating group, or a symmetric group or an abelian group. We moreover extend these results to regular surfaces isogenous to a higher product of curves. 相似文献
15.
Sebastian Casalaina-Martin 《Mathematische Zeitschrift》2008,260(1):115-125
This paper extends joint work with R. Friedman to show that the closure of the locus of intermediate Jacobians of smooth cubic
threefolds, in the moduli space of principally polarized abelian varieties (ppavs) of dimension five, is an irreducible component
of the locus of ppavs whose theta divisor has a point of multiplicity three or more. This paper also gives a sharp bound on
the multiplicity of a point on the theta divisor of an indecomposable ppav of dimension less than or equal to 5; for dimensions
four and five, this improves the bound due to J. Kollár, R. Smith-R. Varley, and L. Ein-R. Lazarsfeld.
The author was partially supported by NSF MSPRF grant DMS-0503228. 相似文献
16.
Paolo Stellari 《Transactions of the American Mathematical Society》2008,360(12):6631-6642
We consider the natural action of a finite group on the moduli space of polarized K3 surfaces which induces a duality defined by Mukai for surfaces of this type. We show that the group permutes polarized Fourier-Mukai partners of polarized K3 surfaces and we study the divisors in the fixed loci of the elements of this finite group.
17.
Sabin Cautis 《Mathematische Annalen》2009,344(3):717-747
Necessary and sufficient conditions are given (in terms of monodromy) for extending a family of smooth curves over an open
subset to a family of stable curves over S. More precisely, we introduce the abelian monodromy extension (AME) property and show that the standard Deligne–Mumford compactification
is the unique, maximal AME compactification of the moduli space of curves. We also show that the Baily–Borel compactification
is the unique, maximal projective AME compactification of the moduli space of abelian varieties. 相似文献
18.
We present a simplified derivation of the fact that the set of gauge equivalence classes or moduli space of flat connections
(potentials) in the abelian Aharonov-Bohm effect, is isomorphic to the circle. The length of this circle is the absolute value
of the electric charge. 相似文献
19.
《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
20.
Christina Birkenhake Hannes Wilhelm 《Transactions of the American Mathematical Society》2003,355(5):1819-1841
A Humbert surface is a hypersurface of the moduli space of principally polarized abelian surfaces defined by an equation of the form with integers . We give geometric characterizations of such Humbert surfaces in terms of the presence of certain curves on the associated Kummer plane. Intriguingly this shows that a certain plane configuration of lines and curves already carries all information about principally polarized abelian surfaces admitting a symmetric endomorphism with given discriminant.