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A symplectic analog of the Quot scheme

Indranil Biswas, Ajneet Dhillon, Jacques Hurtubise, Richard A. Wentworth
2015 Comptes rendus. Mathematique  
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]

Indranil Biswas, Ajneet Dhillon, Jacques Hurtubise, Richard A. Wentworth
2015 arXiv   pre-print
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]

Indranil Biswas, Sorin Dumitrescu, Manfred Lehn
2018 arXiv   pre-print
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

Indranil Biswas, Sorin Dumitrescu, Manfred Lehn
2018 Comptes rendus. Mathematique  
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]

S.Subramanian
2006 arXiv   pre-print
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

Vakkas Ulucay, Mehmet Sahin, Necati Olgun
2018 New Trends in Mathematical Sciences  
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

Indranil Biswas, Ajneet Dhillon, Jacques Hurtubise, Richard A. Wentworth
2015 Advances in Theoretical and Mathematical Physics  
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]

Indranil Biswas, Ajneet Dhillon, Jacques Hurtubise, Richard Wentworth
2014 arXiv   pre-print
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

Дациберг Гонсалвес, Питер Вонг, Сюэчжи Чжао
2020 Чебышевский сборник  
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]

Indranil Biswas, Sorin Dumitrescu
2018 arXiv   pre-print
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 $SL(2, \mathbb{C})$

Indranil Biswas, Avijit Mukherjee
2013 Advances in Theoretical and Mathematical Physics  
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 anddegree(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]

Indranil Biswas, Avijit Mukherjee
2013 arXiv   pre-print
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, anddegree(V ) = 0.  ... 
arXiv:1303.3167v2 fatcat:bkovf7lefnecbbxbl4rvrikxaa

Homomorphisms of connectome graphs [article]

Peteris Daugulis
2014 arXiv   pre-print
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]

Indranil Biswas
2020 arXiv   pre-print
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]

Indranil Biswas, A. J. Parameswaran
2007 arXiv   pre-print
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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