scholarly journals G-marked moduli spaces

2018 ◽  
Vol 20 (06) ◽  
pp. 1750061 ◽  
Author(s):  
Binru Li
Keyword(s):  
Finite Group ◽  
Moduli Spaces ◽  
Effective Action ◽  
Canonical Representation ◽  
Hilbert Polynomial ◽  
Projective Varieties ◽  
Canonical Models ◽  
Decomposition Formula ◽  
Polynomial Formula ◽  
Type Decomposition

The aim of this paper is to investigate the closed subschemes of moduli spaces corresponding to projective varieties which admit an effective action by a given finite group [Formula: see text]. To achieve this, we introduce the moduli functor [Formula: see text] of [Formula: see text]-marked Gorenstein canonical models with Hilbert polynomial [Formula: see text], and prove the existence of [Formula: see text], the coarse moduli scheme for [Formula: see text]. Then we show that [Formula: see text] has a proper and finite morphism onto [Formula: see text] so that its image [Formula: see text] is a closed subscheme. In the end we obtain the canonical representation type decomposition [Formula: see text] of [Formula: see text] and use [Formula: see text] to study the structure of [Formula: see text].

scholarly journals COHERENT SYSTEMS AND MODULAR SUBAVRIETIES OF $\mathcal{SU}_C(r)$

2012 ◽  
Vol 23 (04) ◽  
pp. 1250037 ◽  
Author(s):  
MICHELE BOLOGNESI ◽  
SONIA BRIVIO
Keyword(s):  
Moduli Spaces ◽  
Vector Bundles ◽  
Low Rank ◽  
Coherent Systems ◽  
Projective Varieties ◽  
Complex Curve ◽  
Smooth Complex ◽  
Moduli Theory ◽  
Modular Varieties ◽  
Small Genus

Let C be an algebraic smooth complex curve of genus g > 1. The object of this paper is the study of the birational structure of certain moduli spaces of vector bundles and of coherent systems on C and the comparison of different type of notions of stability arising in moduli theory. Notably we show that in certain cases these moduli spaces are birationally equivalent to fibrations over simple projective varieties, whose fibers are GIT quotients (ℙr-1)rg// PGL (r), where r is the rank of the considered vector bundles. This allows us to compare different definitions of (semi-)stability (slope stability, α-stability, GIT stability) for vector bundles, coherent systems and point sets, and derive relations between them. In certain cases of vector bundles of low rank when C has small genus, our construction produces families of classical modular varieties contained in the Coble hypersurfaces.

scholarly journals On the Singular Sheaves in the Fine Simpson Moduli Spaces of 1-dimensional Sheaves

2017 ◽  
Vol 60 (3) ◽  
pp. 522-535 ◽  
Author(s):  
Oleksandr Iena ◽  
Alain Leytem
Keyword(s):  
Projective Plane ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Blow Up ◽  
Line Bundles ◽  
Hilbert Polynomial ◽  
Stable Sheaves ◽  
Closed Subvariety

AbstractIn the Simpson moduli space M of semi-stable sheaves with Hilbert polynomial dm − 1 on a projective plane we study the closed subvariety M' of sheaves that are not locally free on their support. We show that for d ≥4 , it is a singular subvariety of codimension 2 in M. The blow up of M along M' is interpreted as a (partial) modification of M \ M' by line bundles (on support).

Moduli of wild Higgs bundles on with -actions

2021 ◽  
pp. 1-34
Author(s):  
LAURA FREDRICKSON ◽  
ANDREW NEITZKE
Keyword(s):  
Fixed Points ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
Central Charge ◽  
Higgs Field ◽  
Vertex Algebra ◽  
Higgs Bundles ◽  
Irregular Singularity ◽  
Isomorphism Classes ◽  
Type Decomposition

Abstract We study a set $\mathcal{M}_{K,N}$ parameterising filtered SL(K)-Higgs bundles over $\mathbb{C}P^1$ with an irregular singularity at $z = \infty$ , such that the eigenvalues of the Higgs field grow like $\vert \lambda \vert \sim \vert z^{N/K} \mathrm{d}z \vert$ , where K and N are coprime. $\mathcal{M}_{K,N}$ carries a $\mathbb{C}^\times$ -action analogous to the famous $\mathbb{C}^\times$ -action introduced by Hitchin on the moduli spaces of Higgs bundles over compact curves. The construction of this $\mathbb{C}^\times$ -action on $\mathcal{M}_{K,N}$ involves the rotation automorphism of the base $\mathbb{C}P^1$ . We classify the fixed points of this $\mathbb{C}^\times$ -action, and exhibit a curious 1-1 correspondence between these fixed points and certain representations of the vertex algebra $\mathcal{W}_K$ ; in particular we have the relation $\mu = {k-1-c_{\mathrm{eff}}}/{12}$ , where $\mu$ is a regulated version of the L 2 norm of the Higgs field, and $c_{\mathrm{eff}}$ is the effective Virasoro central charge of the corresponding W-algebra representation. We also discuss a Białynicki–Birula-type decomposition of $\mathcal{M}_{K,N}$ , where the strata are labeled by isomorphism classes of the underlying filtered vector bundles.

scholarly journals Chow instability of certain projective varieties

1983 ◽  
Vol 92 ◽  
pp. 39-50 ◽  
Author(s):  
Shihoko Ishii
Keyword(s):  
Moduli Spaces ◽  
Projective Variety ◽  
Ample Divisor ◽  
Projective Varieties

A pair (X, D) of a projective variety X and a very ample divisor D on X is called stable (resp. semi-stable, resp. unstable) if the Chow point corresponding to the embedding is SL(N + 1)-stable (resp. semi-stable, resp. unstable). The criterion for stability is one of the most important steps in proving the existence of moduli spaces.

Jordan property and automorphism groups of normal compact Kähler varieties

2018 ◽  
Vol 20 (03) ◽  
pp. 1750024 ◽  
Author(s):  
Jin Hong Kim
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Projective Varieties ◽  
Full Automorphism Group ◽  
Identity Component ◽  
Arbitrary Dimensions ◽  
Type Decomposition

It has been recently shown by Meng and Zhang that the full automorphism group [Formula: see text] is a Jordan group for all projective varieties in arbitrary dimensions. The aim of this paper is to show that the full automorphism group [Formula: see text] is, in fact, a Jordan group even for all normal compact Kähler varieties in arbitrary dimensions. The meromorphic structure of the identity component of the automorphism group and its Rosenlicht-type decomposition play crucial roles in the proof.

scholarly journals Ekedahl-Oort Strata for Good Reductions of Shimura Varieties of Hodge Type

2018 ◽  
Vol 70 (2) ◽  
pp. 451-480 ◽  
Author(s):  
Chao Zhang
Keyword(s):  
Weyl Group ◽  
Moduli Spaces ◽  
Level Structure ◽  
Reductive Group ◽  
Extension Property ◽  
Integral Model ◽  
Shimura Varieties ◽  
Shimura Variety ◽  
Canonical Models ◽  
Special Fibers

AbstractFor a Shimura variety of Hodge type with hyperspecial level structure at a prime p, Vasiu and Kisin constructed a smooth integral model (namely the integral canonical model) uniquely determined by a certain extension property. We define and study the Ekedahl-Oort stratifications on the special fibers of those integral canonical models when p > 2. This generalizes Ekedahl-Oort stratifications defined and studied by Oort on moduli spaces of principally polarized abelian varieties and those defined and studied by Moonen, Wedhorn, and Viehmann on good reductions of Shimura varieties of PEL type. We show that the Ekedahl-Oort strata are parameterized by certain elements w in the Weyl group of the reductive group in the Shimura datum. We prove that the stratum corresponding to w is smooth of dimension l(w) (i.e., the length of w) if it is non-empty. We also determine the closure of each stratum.

scholarly journals A higher-dimensional generalization of Lichtenbaum duality in terms of the Albanese map

2016 ◽  
Vol 152 (9) ◽  
pp. 1915-1934 ◽  
Author(s):  
Wataru Kai
Keyword(s):  
Finite Group ◽  
Integral Model ◽  
Brauer Groups ◽  
Comparison Result ◽  
Projective Varieties ◽  
Higher Dimensional ◽  
Albanese Map ◽  
A Finite Group ◽  
Smooth Projective Varieties ◽  
Local Side

In this article, we present a conjectural formula describing the cokernel of the Albanese map of zero-cycles of smooth projective varieties $X$ over $p$-adic fields in terms of the Néron–Severi group and provide a proof under additional assumptions on an integral model of $X$. The proof depends on a non-degeneracy result of Brauer–Manin pairing due to Saito–Sato and on Gabber–de Jong’s comparison result of cohomological and Azumaya–Brauer groups. We will also mention the local–global problem for the Albanese cokernel; the abelian group on the ‘local side’ turns out to be a finite group.

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