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A symplectic analog of the Quot scheme
2015
Comptes rendus. Mathematique
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We construct a symplectic analog of the Quot scheme that parameterizes the torsion quotients of a trivial vector bundle over a compact Riemann surface. ...
Some of its properties are investigated. © 2015 Académie des sciences. Published by Elsevier Masson SAS. ...
Take torsion quotients of it of degree dr that are compatible with the symplectic structure (this is explained in Section 2.1). Fixing X , r and d, let Q denote the associated symplectic Quot scheme. ...
doi:10.1016/j.crma.2015.09.006
fatcat:vd7h3kwcorgq7epotijwx5ikqy
A symplectic analog of the Quot scheme
[article]
2015
arXiv
pre-print
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We construct a symplectic analog of the Quot scheme that parametrizes the torsion quotients of a trivial vector bundle over a compact Riemann surface. Some of its properties are investigated. ...
Take torsion quotients of it of degree dr that are compatible with the symplectic structure (this is explained in Section 2.1). Fixing X, r and d, let Q denote the associated symplectic Quot scheme. ...
For fixed integers n and d, let Q(O ⊕n X , d) denote the Quot scheme that parametrizes the torsion quotients of O ⊕n X of degree d (see [8] for construction and properties of a general Quot schemes). ...
arXiv:1509.03952v1
fatcat:4gndkthfqzf7lifjpdmeuxwcha
On the stability of flat complex vector bundles over parallelizable manifolds
[article]
2018
arXiv
pre-print
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All the rational Chern classes of E vanish, in particular, its degree is zero. We deduce a stability result for flat holomorphic vector bundles E_ρ of rank 2 over G/ Γ. ...
If an irreducible representation ρ : Γ→GL(2, C) satisfies the conditionmthat the induced homomorphism Γ→ PGL(2, C) does not extend to a homomorphism from G, then E_ρ is proved to be stable. ...
Consider the translations of h by the right-multiplication action of G on itself. The resulting Hermitian structure on G descends to a Hermitian structure on the quotient M in (2.1). ...
arXiv:1709.05951v2
fatcat:djzgn36ksfhdrp4c7zxhju7ihu
On the stability of flat complex vector bundles over parallelizable manifolds
2018
Comptes rendus. Mathematique
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All the rational Chern classes of E vanish, in particular, its degree is zero. We deduce a stability result for flat holomorphic vector bundles E ρ of rank 2 over G/Γ. ...
If an irreducible representation ρ : Γ −→ GL(2, C) satisfies the condition that the induced homomorphism Γ −→ PGL(2, C) does not extend to a homomorphism from G, then E ρ is proved to be stable. 2000 Mathematics ...
Consider the translations of h by the right-multiplication action of G on itself. The resulting Hermitian structure on G descends to a Hermitian structure on the quotient M in (2.1). ...
doi:10.1016/j.crma.2018.08.001
fatcat:dz3qhgwmezg3pp6gytoffaj2te
Strongly Semistable Bundles on a Curve over a finite field
[article]
2006
arXiv
pre-print
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We show that a principal G bundle on a smooth projective curve over a finite field is strongly semistable if and only if it is defined by a representation of the fundamental group scheme of the curve into ...
and a reduction of structure group E e H ⊂ E of degree zero with H ⊂ M. ...
of π(X l , x) invariant under the action of Gal(l/k) on π(X l , x) descends to a quotient of π(X, x).Hence H is a quotient of π(X, x) and we obtain the homomorphism π(X, x) → G defining E on X over k. ...
arXiv:math/0611212v1
fatcat:hhtc3hcbfraebktp2yqtgj3nhu
Normed quotient rings
2018
New Trends in Mathematical Sciences
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In this article, we introduce the notions of normed quotient ring, normed quotient subring, normed quotient ring homomorphism, normed quotient ring natural homomorphism and investigate some of their related ...
Utumi [26] R has always a unique maximal left quotient ring, and moreover the maximal left quotient ring of a total matrix ring of finite degree over R is a total matrix ring of the same degree over ...
They also investigated the connections between the ideal structure of an arbitrary ring R and the ideal structure of Q(R). ...
doi:10.20852/ntmsci.2018.245
fatcat:tqhy4dmuafgdpat34nzmyjn6jq
A generalized Quot scheme and meromorphic vortices
2015
Advances in Theoretical and Mathematical Physics
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Consider all pairs of the form (F, f), where F is a holomorphic vector bundle on X of rank r and degree d z − d p , and is a meromorphic homomorphism which an isomorphism outside a finite subset of X and ...
has pole (respectively, zero) of total degree d p (respectively, d z ). ...
Acknowledgements We thank the National University of Singapore for its hospitality. ...
doi:10.4310/atmp.2015.v19.n4.a6
fatcat:um6asaso6zek7jgpii3kapmb3u
A generalized Quot scheme and meromorphic vortices
[article]
2014
arXiv
pre-print
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Consider all pairs of the form (F, f), where F is a holomorphic vector bundle on X of rank r and degree d_z-d_p, and f : O^⊕ r_X → F is a meromorphic homomorphism which an isomorphism outside a finite ...
subset of X and has pole (respectively, zero) of total degree d_p (respectively, d_z). ...
Acknowledgements We thank the National University of Singapore for its hospitality. ...
arXiv:1410.1182v1
fatcat:jnogo4s54bdd3dzvxfp77glf54
Степени отображений между гомотопическими пространственными формами
2020
Чебышевский сборник
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The ring structure follows promptly from the ring structure of the cohomology ring * ( , Z) and dimensional reason. ...
Let = where , have orders relatively prime, for = 1, 2, and : 1 → 2 a homomorphism such that ( 1 ) ⊂ 2 , and denote by¯the induced homomorphism on the quotient 1 / 1 → 2 / 2 . ...
Since the induced map on the quotient Z 2 → Z 2 is the homomorphism sending 1 to 2 , the induced in dimension on 2 is multiplication by 2 −1 and on 4 is multiplication by 2 2 −2 , which is degree 0 except ...
doi:10.22405/2226-8383-2020-21-2-94-108
fatcat:cemqycazjvfnfkguoyd5bgarre
Branched holomorphic Cartan geometries and Calabi-Yau manifolds
[article]
2018
arXiv
pre-print
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The key ingredient of its proof is the following result of independent interest: If E is a holomorphic vector bundle over a compact simply connected K\"ahler Calabi-Yau manifold, and E admits a holomorphic ...
We also give an example of a non-flat branched holomorphic normal projective structure on a compact complex surface. ...
He thanks the Université Côte d'Azur and Dieudonné Department of Mathematics for their hospitality. ...
arXiv:1706.04407v2
fatcat:73cp4hurdjbengenvtxqjjlmrm
On the vector bundles associated to the irreducible representations of cocompact lattices of $SL(2, \mathbb{C})$
2013
Advances in Theoretical and Mathematical Physics
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The compact complex manifold SL(2, C)/Γ has natural Hermitian structures; the polystability of E ρ is with respect to these natural Hermitian structures. ...
We prove the following: let Γ ⊂ SL(2, C) be a cocompact lattice and let ρ : Γ −→ GL(r, C) be an irreducible representation. ...
Consider all nonzero coherent analytic subsheaves V of E ρ such that • V is polystable and • degree(V ) = 0. ...
doi:10.4310/atmp.2013.v17.n6.a7
fatcat:ek4fvow6n5cavd4inzwz4spape
On the vector bundles associated to irreducible representations of cocompact lattices of SL(2,C)
[article]
2013
arXiv
pre-print
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The compact complex manifold SL(2, C)/Γ has natural Hermitian structures; the polystability of E_ρ is with respect to these natural Hermitian structures. ...
In this continuation of BM, we prove the following: Let Γ⊂SL(2, C) be a cocompact lattice, and let ρ: Γ→GL(r, C) be an irreducible representation. ...
Consider all nonzero coherent analytic subsheaves V of E ρ such that • V is polystable, and • degree(V ) = 0. ...
arXiv:1303.3167v2
fatcat:bkovf7lefnecbbxbl4rvrikxaa
Homomorphisms of connectome graphs
[article]
2014
arXiv
pre-print
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We propose to study homomorphisms of connectome graphs. Homomorphisms can be studied as sequences of elementary homomorphisms - folds, which identify pairs of vertices. ...
known properties of "rich club" (various centrality invariants) in terms of terminal graph structures; 5. study structure of strongly connected components of connectomes and their images under homomorphisms ...
Noninjective homomorphisms preserve graph structure and decrease the number of vertices. Thus homomorphisms may be used to analyze big graphs such as connectome graphs. ...
arXiv:1412.3064v1
fatcat:xhhtwfmlkjhmdj4p6j3swnqbea
Abel-Jacobi map and curvature of the pulled back metric
[article]
2020
arXiv
pre-print
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We investigate the curvature of the pull-back, by φ, of the flat metric on Pic^d(X). ...
In particular, we show that when d=1, the curvature is strictly negative everywhere if X is not hyperelliptic, and when X is hyperelliptic, the curvature is nonpositive with vanishing exactly on the points ...
We will show that the homomorphisms α ′ , β ′ , δ ′ x and ν ′ in (3.5) are duals of the homomorphisms α, β, δ x and ν respectively, which are constructed in (2.5) . ...
arXiv:2004.04893v1
fatcat:awyzmahs25ay7mic7yc6vodbfa
Monodromy group for a strongly semistable principal bundle over a curve, II
[article]
2007
arXiv
pre-print
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The group scheme M is canonically a quotient of G_X, and E_M is the extension of structure group of E_ G_X. ...
We associate to E_G a group scheme M defined over k, which we call the monodromy group scheme of E_G, and a principal M-bundle E_M over X, which we call the monodromy bundle of E_G. ...
The referee gave detailed comments how the results (of a previous version) could be generalized. The referee also gave suggestions to improve the exposition. We are very grateful to the referee. ...
arXiv:math/0601768v2
fatcat:ur3xunsmungglbo5yk7cmzac4q
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