A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
A symplectic analog of the Quot scheme

2015
*
Comptes rendus. Mathematique
*

We construct a symplectic analog

doi:10.1016/j.crma.2015.09.006
fatcat:vd7h3kwcorgq7epotijwx5ikqy
*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. ...##
###
A symplectic analog of the Quot scheme
[article]

2015
*
arXiv
*
pre-print

We construct a symplectic analog

arXiv:1509.03952v1
fatcat:4gndkthfqzf7lifjpdmeuxwcha
*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). ...##
###
On the stability of flat complex vector bundles over parallelizable manifolds
[article]

2018
*
arXiv
*
pre-print

All the rational Chern classes

arXiv:1709.05951v2
fatcat:djzgn36ksfhdrp4c7zxhju7ihu
*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). ...##
###
On the stability of flat complex vector bundles over parallelizable manifolds

2018
*
Comptes rendus. Mathematique
*

All the rational Chern classes

doi:10.1016/j.crma.2018.08.001
fatcat:dz3qhgwmezg3pp6gytoffaj2te
*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). ...##
###
Strongly Semistable Bundles on a Curve over a finite field
[article]

2006
*
arXiv
*
pre-print

We show that a principal G bundle on a smooth projective curve over a finite field is strongly semistable if

arXiv:math/0611212v1
fatcat:hhtc3hcbfraebktp2yqtgj3nhu
*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. ...##
###
Normed quotient rings

2018
*
New Trends in Mathematical Sciences
*

In this article, we introduce the notions

doi:10.20852/ntmsci.2018.245
fatcat:tqhy4dmuafgdpat34nzmyjn6jq
*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). ...##
###
A generalized Quot scheme and meromorphic vortices

2015
*
Advances in Theoretical and Mathematical Physics
*

Consider all pairs

doi:10.4310/atmp.2015.v19.n4.a6
fatcat:um6asaso6zek7jgpii3kapmb3u
*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. ...##
###
A generalized Quot scheme and meromorphic vortices
[article]

2014
*
arXiv
*
pre-print

Consider all pairs

arXiv:1410.1182v1
fatcat:jnogo4s54bdd3dzvxfp77glf54
*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. ...##
###
Степени отображений между гомотопическими пространственными формами

2020
*
Чебышевский сборник
*

The ring

doi:10.22405/2226-8383-2020-21-2-94-108
fatcat:cemqycazjvfnfkguoyd5bgarre
*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 ...##
###
Branched holomorphic Cartan geometries and Calabi-Yau manifolds
[article]

2018
*
arXiv
*
pre-print

The key ingredient

arXiv:1706.04407v2
fatcat:73cp4hurdjbengenvtxqjjlmrm
*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. ...##
###
On the vector bundles associated to the irreducible representations of cocompact lattices of $SL(2, \mathbb{C})$

2013
*
Advances in Theoretical and Mathematical Physics
*

The compact complex manifold SL(2, C)/Γ has natural Hermitian

doi:10.4310/atmp.2013.v17.n6.a7
fatcat:ek4fvow6n5cavd4inzwz4spape
*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. ...##
###
On the vector bundles associated to irreducible representations of cocompact lattices of SL(2,C)
[article]

2013
*
arXiv
*
pre-print

The compact complex manifold SL(2, C)/Γ has natural Hermitian

arXiv:1303.3167v2
fatcat:bkovf7lefnecbbxbl4rvrikxaa
*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. ...##
###
Homomorphisms of connectome graphs
[article]

2014
*
arXiv
*
pre-print

We propose to study

arXiv:1412.3064v1
fatcat:xhhtwfmlkjhmdj4p6j3swnqbea
*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. ...##
###
Abel-Jacobi map and curvature of the pulled back metric
[article]

2020
*
arXiv
*
pre-print

We investigate the curvature

arXiv:2004.04893v1
fatcat:awyzmahs25ay7mic7yc6vodbfa
*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) . ...##
###
Monodromy group for a strongly semistable principal bundle over a curve, II
[article]

2007
*
arXiv
*
pre-print

The group scheme M is canonically a

arXiv:math/0601768v2
fatcat:ur3xunsmungglbo5yk7cmzac4q
*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. ...
« Previous

*Showing results 1 — 15 out of 56,460 results*