Hodge polynomials of SL $$(2,\mathbb{C })$$ -character varieties for curves of small genus

2013 ◽  
Vol 26 (2) ◽  
pp. 635-703 ◽  
Author(s):  
Marina Logares ◽  
Vicente Muñoz ◽  
P. E. Newstead
Keyword(s):  
Character Varieties ◽  
Hodge Polynomials ◽  
Small Genus

MIXED HODGE STRUCTURES OF THE MODULI SPACES OF PARABOLIC CONNECTIONS

2016 ◽  
Vol 225 ◽  
pp. 185-206
Author(s):  
ARATA KOMYO
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Higgs Bundles ◽  
Hodge Structures ◽  
Character Varieties ◽  
Generic Eigenvalues ◽  
Hodge Polynomials ◽  
Mixed Hodge Structures

In this paper, we investigate the mixed Hodge structures of the moduli space of $\boldsymbol{\unicode[STIX]{x1D6FC}}$-stable parabolic Higgs bundles and the moduli space of $\boldsymbol{\unicode[STIX]{x1D6FC}}$-stable regular singular parabolic connections. We show that the mixed Hodge polynomials are independent of the choice of generic eigenvalues and the mixed Hodge structures of these moduli spaces are pure. Moreover, by the Riemann–Hilbert correspondence, the Poincaré polynomials of character varieties are independent of the choice of generic eigenvalues.

scholarly journals Mixed Hodge polynomials of character varieties

2008 ◽  
Vol 174 (3) ◽  
pp. 555-624 ◽  
Author(s):  
Tamás Hausel ◽  
Fernando Rodriguez-Villegas
Keyword(s):  
Character Varieties ◽  
Hodge Polynomials

scholarly journals Topological mirror symmetry for rank two character varieties of surface groups

2021 ◽  
Author(s):  
Mirko Mauri
Keyword(s):  
Moduli Spaces ◽  
Mirror Symmetry ◽  
Surface Groups ◽  
Character Varieties ◽  
Hitchin System ◽  
Global Topology ◽  
Hodge Numbers

AbstractThe moduli spaces of flat $${\text{SL}}_2$$ SL 2 - and $${\text{PGL}}_2$$ PGL 2 -connections are known to be singular SYZ-mirror partners. We establish the equality of Hodge numbers of their intersection (stringy) cohomology. In rank two, this answers a question raised by Tamás Hausel in Remark 3.30 of “Global topology of the Hitchin system”.

A new synonym of Ptilagrostis yadongensis and a new record of Stipa bhutanica to the flora of China (Poaceae)

Phytotaxa ◽  
2016 ◽  
Vol 272 (1) ◽  
pp. 94 ◽  
Author(s):  
ZHONG-SHUAI ZHANG ◽  
XIANG-YUN ZHU ◽  
LING-LU LI ◽  
SHAN-WEN JIANG ◽  
WEN-LI CHEN
Keyword(s):  
North America ◽  
New Record ◽  
Tibet Plateau ◽  
Southern Slope ◽  
Chinese Journal ◽  
Grass Family ◽  
New Synonym ◽  
Flora Of China ◽  
Qinghai Tibet Plateau ◽  
Small Genus

Ptilagrostis Grisebach (1852: 447) is a small genus of the grass family, including approximately 11 species (Wu & Phillips 2006, Barkworth 2007). It occurs in both Asia and North America with about eight species distributed in Qinghai-Tibet Plateau, its diversity center. Ptilagrostis yadongensis Keng & Tang (1985: 44) is one of the species that occurs in this region, which was described based on materials from Yadong, China, the southern slope of Himalayas. The paper was published in a Chinese journal, viz. Journal of Southwest Agriculural University, and had not been noticed until 2005 (Peterson et al. 2005, Wu & Phillips 2006). The author pointed out that P. yadongensis is distinguished from its morphological close, Ptilagrostis concinna (Hooker 1897: 230) Roshevitz (1934: 75) by linear panicles with fewer spikelets, longer and unequal glumes, and shorter and glabrous anthers.

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.

The southern Palearctic genus Enneastigma Stein (Diptera: Anthomyiidae): Taxonomy of Mediterranean species, phylogeny and ancestral areas analysis

1994 ◽  
Vol 25 (4) ◽  
pp. 361-375 ◽  
Author(s):  
Verner Michelsen
Keyword(s):  
Cladistic Analysis ◽  
Alternative Methods ◽  
Mediterranean Species ◽  
Species Phylogeny ◽  
Males And Females ◽  
The Mediterranean ◽  
Small Genus

AbstractEnneastigma is a small genus of myopinine anthomyiids which comprises five species in the Mediterranean subregion (E. compressum Stein, E. rarum sp. n., E. rufitibia sp. n., E. triplex Loew, E. triseriatum Stein) and two species in SE Palearctic part of China (E. pilosiventrosum Fan & Chen, E. shanghaiensis Fan & Chen). All species appear to be univoltine and only active during the cooler parts of the season. The larvae may all be coprophagous. The Mediterranean species are revised with keys to males and females and illustrated descriptions of males, females and eggs. One lectotype is designated. A cladistic analysis was conducted which also included the Chinese species. This resulted in a single, most parsimonious phylogeny. The resulting area cladogram was used to assess the alternative methods for estimating ancestral areas as proposed recently by K. Bremer and F. Ronquist. It is concluded that the best results are obtained by using a refined Ronquist analysis.

Toric Geometry ofSL2(ℂ) Free Group Character Varieties from Outer Space

2018 ◽  
Vol 70 (2) ◽  
pp. 354-399 ◽  
Author(s):  
Christopher Manon
Keyword(s):  
Free Group ◽  
Outer Space ◽  
Integrable Hamiltonian System ◽  
Outer Automorphism ◽  
Character Variety ◽  
Toric Geometry ◽  
Character Varieties ◽  
Simplicial Space ◽  
Proper Map ◽  
Divisorial Valuations

AbstractCuller and Vogtmann defined a simplicial spaceO(g), calledouter space, to study the outer automorphism group of the free groupFg. Using representation theoretic methods, we give an embedding ofO(g) into the analytification of X(Fg,SL2(ℂ)), theSL2(ℂ) character variety ofFg, reproving a result of Morgan and Shalen. Then we show that every pointvcontained in a maximal cell ofO(g) defines a flat degeneration of X(Fg,SL2(ℂ)) to a toric varietyX(PΓ). We relate X(Fg,SL2(ℂ)) andX(v) topologically by showing that there is a surjective, continuous, proper map Ξv:X(Fg,SL2(ℂ)) →X(v). We then show that this map is a symplectomorphism on a dense open subset of X(Fg, SL2(ℂ)) with respect to natural symplectic structures on X(Fg, SL2(ℂ)) andX(v). In this way, we construct an integrable Hamiltonian system in X(Fg, SL2(ℂ)) for each point in a maximal cell ofO(g), and we show that eachvdefines a topological decomposition of X(Fg, SL2(ℂ)) derived from the decomposition ofX(PΓ) by its torus orbits. Finally, we show that the valuations coming from the closure of a maximal cell inO(g) all arise as divisorial valuations built from an associated projective compactification of X(Fg, SL2(ℂ)).

scholarly journals Morphology, evolution and taxonomy of Wachendorfia (Haemodoraceae)

Bothalia ◽  
1992 ◽  
Vol 22 (1) ◽  
pp. 59-57 ◽  
Author(s):  
N. E. Helme ◽  
H. P. Linder
Keyword(s):  
Ecological Speciation ◽  
Morphology Evolution ◽  
Distribution Maps ◽  
Speciation Model ◽  
Taxonomic Descriptions ◽  
Infraspecific Taxa ◽  
Cape Floral Region ◽  
Variable Species ◽  
Rhizome Morphology ◽  
Small Genus

Wachendorfia Burm. is a small genus endemic to the Cape Floral Region. Pour species are recognised in this study. Two species were originally described by Burman in 1757 and these were followed by numerous other descriptions of what is essentially one very variable species  (W. paniculaia Burm.). This variation is discussed and reasons are given as to why the recognition of formal infraspecific taxa is inappropriate. Formal taxonomic descriptions, distribution maps and a key to the species are provided. Rhizome morphology, leaf anatomy and pollen and seed coat structures were investigated and illustrations are provided. A cladogram was inferred and this is consistent with an ecological speciation model for the genus. The two species with the most restricted distribution (W. brachyandra W.F. Barker and W. pamfiora W.F. Barker) are considered to be the most recently evolved. Features of systematic and ecological interest (e.g. floral enantiomorphy) are discussed.

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