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E Ballico - One of the best experts on this subject based on the ideXlab platform.
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c © 1998 Universitat de Barcelona The Subbundles of decomposable vector bundles over an elliptic curve
2015Co-Authors: E Ballico, Dedicated To F. SerranoAbstract:Let C be an elliptic curve and E, F polystable vector bundles on C such that no two among the indecomposable factors of E ⊕ F are isomorphic. Here we give a complete classification of such pairs (E,F) such that E is a subbundle of F. In [1] M. Atiyah classified the vector bundles over an elliptic curve C. But still, there are several natural open questions on the structure of the Subbundles of a fixed vector bundle on C. The aim of this paper is to give a reasonably complete answer to this question restricting slightly the vector bundles involved (see Corollary 0.2). A vector bundle F on a smooth projective curve is called polystable if it is the direct sum of stable vector bundles with the same slope µ(F). In particular a polystable vector bundle is semistable. The notion of polystability is very natural over an elliptic curve, because very few vector bundles over an elliptic curve are stable, while for all integers r, d with r> 0 there exist polystable vector bundles with rank r and degree d. All this paper is devoted to the proof of the following result. Theorem 0.1 Fix integers x, y, ai, 1 ≤ i ≤ x, ri, 1 ≤ i ≤ x, bj, 1 ≤ j ≤ y, sj, 1 ≤ j ≤ y, with x> 0, y> 0, ri> 0 for every i, sj> 0 for every j and ai/ri < bj/sj for every i and every j. Let C be an elliptic curve. Fix polystable vector bundles Ei, 1 ≤ i ≤ x, and Fj, 1 ≤ j ≤ y, with rank(Ei) = ri, deg(Ei) = ai, rank(Fj) = sj
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maximal Subbundles of rank 2 vector bundles on projective curves
Canadian Mathematical Bulletin, 2000Co-Authors: E BallicoAbstract:Let be a stable rank 2 vector bundle on a smooth projective curve and be the set of all rank 1 Subbundles of with maximal degree. Here we study the varieties (non-emptyness, irreducibility and dimension) of all rank 2 stable vector bundles, , on with fixed and and such that .
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stable bundles on projective curves their filtrations and their Subbundles
Pacific Journal of Mathematics, 1998Co-Authors: E BallicoAbstract:Let X be a smooth genus g projective curve. Here we study the maximal degree Subbundles of the stable vector bundles on X and the existence of stable vector bundles on X with suitable ltrations by Subbundles. Tools: Elementary transformations of vector bundles and pull-backs of bundles from lower genus curves.
George H Hitching - One of the best experts on this subject based on the ideXlab platform.
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counting maximal lagrangian Subbundles over an algebraic curve
Journal of Geometry and Physics, 2021Co-Authors: Daewoong Cheong, Insong Choe, George H HitchingAbstract:Abstract Let C be a smooth projective curve and W a symplectic bundle over C. Let L Q e ( W ) be the Lagrangian Quot scheme parametrizing Lagrangian subsheaves E ⊂ W of degree e. We give a closed formula for intersection numbers on L Q e ( W ) . As a special case, for g ≥ 2 , we compute the number of Lagrangian Subbundles of maximal degree of a general stable symplectic bundle, when this is finite. This is a symplectic analogue of Holla's enumeration of maximal Subbundles in [14] .
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counting maximal lagrangian Subbundles over an algebraic curve
arXiv: Algebraic Geometry, 2019Co-Authors: Daewoong Cheong, Insong Choe, George H HitchingAbstract:Let $C$ be a smooth projective curve and $W$ a symplectic bundle over $C$. Let $LQ_e (W)$ be the Lagrangian Quot scheme parametrizing Lagrangian subsheaves $E \subset W$ of degree $e$. We give a closed formula for intersection numbers on $LQ_e (W)$. As a special case, for $g \ge 2$, we compute the number of Lagrangian Subbundles of maximal degree of a general stable symplectic bundle, when this is finite. This is a symplectic analogue of Holla's enumeration of maximal Subbundles in [13].
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non defectivity of grassmannian bundles over a curve
arXiv: Algebraic Geometry, 2015Co-Authors: Insong Choe, George H HitchingAbstract:Let Gr(2, E) be the Grassmann bundle of two-planes associated to a general bundle E over a curve X. We prove that an embedding of Gr(2, E) by a certain twist of the relative Pl\"ucker map is not secant defective. This yields a new and more geometric proof of the Hirschowitz-type bound on the Lagrangian Segre invariant for orthogonal bundles over X, analogous to those given for vector bundles and symplectic bundles in [2, 3]. From the non-defectivity we also deduce an interesting feature of a general orthogonal bundle over X, contrasting with the classical and symplectic cases: Any maximal Lagrangian subbundle intersects at least one other maximal Lagrangian subbundle in positive rank.
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lagrangian Subbundles of orthogonal bundles of odd rank over an algebraic curve
arXiv: Algebraic Geometry, 2014Co-Authors: Insong Choe, George H HitchingAbstract:An orthogonal bundle over a curve has an isotropic Segre invariant determined by the maximal degree of a Lagrangian subbundle. This invariant, and the induced stratifications on moduli spaces of orthogonal bundles, were studied for bundles of even rank in [4]. In this paper, we obtain analogous results for bundles of odd rank. We obtain a sharp upper bound on the isotropic Segre invariant. We show the irreducibility of the induced strata on the moduli spaces of orthogonal bundles of odd rank, and compute their dimensions. As a key ingredient of the proofs, we study the correspondence between Lagrangian Subbundles of orthogonal bundles of even and odd rank.
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lagrangian Subbundles of symplectic bundles over a curve
Mathematical Proceedings of the Cambridge Philosophical Society, 2012Co-Authors: Insong Choe, George H HitchingAbstract:A symplectic bundle over an algebraic curve has a natural invariant s Lag determined by the maximal degree of its Lagrangian Subbundles. This can be viewed as a generalization of the classical Segre invariants of a vector bundle. We give a sharp upper bound on s Lag which is analogous to the Hirschowitz bound on the classical Segre invariants. Furthermore, we study the stratifications induced by s Lag on moduli spaces of symplectic bundles, and get a full picture for the case of rank four.
Viola Vogel - One of the best experts on this subject based on the ideXlab platform.
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Vogel V (2008) How force might activate talin’s vinculin binding sites: SMD reveals a structural mechanism. PLoS Comput Biol 4: e24
2016Co-Authors: Vesa P. Hytönen, Viola VogelAbstract:Upon cell adhesion, talin physically couples the cytoskeleton via integrins to the extracellular matrix, and subsequent vinculin recruitment is enhanced by locally applied tensile force. Since the vinculin binding (VB) sites are buried in the talin rod under equilibrium conditions, the structural mechanism of how vinculin binding to talin is force-activated remains unknown. Taken together with experimental data, a biphasic vinculin binding model, as derived from steered molecular dynamics, provides high resolution structural insights how tensile mechanical force applied to the talin rod fragment (residues 486–889 constituting helices H1–H12) might activate the VB sites. Fragmentation of the rod into three helix Subbundles is prerequisite to the sequential exposure of VB helices to water. Finally, unfolding of a VB helix into a completely stretched polypeptide might inhibit further binding of vinculin. The first events in fracturing the H1– H12 rods of talin1 and talin2 in Subbundles are similar. The proposed force-activated a-helix swapping mechanism by which vinculin binding sites in talin rods are exposed works distinctly different from that of other force-activated bonds, including catch bonds
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How force might activate talin's vinculin binding sites: SMD reveals a structural mechanism
PLoS Computational Biology, 2008Co-Authors: Vesa P. Hytönen, Viola VogelAbstract:Upon cell adhesion, talin physically couples the cytoskeleton via integrins to the extracellular matrix, and subsequent vinculin recruitment is enhanced by locally applied tensile force. Since the vinculin binding (VB) sites are buried in the talin rod under equilibrium conditions, the structural mechanism of how vinculin binding to talin is force-activated remains unknown. Taken together with experimental data, a biphasic vinculin binding model, as derived from steered molecular dynamics, provides high resolution structural insights how tensile mechanical force applied to the talin rod fragment (residues 486-889 constituting helices H1-H12) might activate the VB sites. Fragmentation of the rod into three helix Subbundles is prerequisite to the sequential exposure of VB helices to water. Finally, unfolding of a VB helix into a completely stretched polypeptide might inhibit further binding of vinculin. The first events in fracturing the H1-H12 rods of talin1 and talin2 in Subbundles are similar. The proposed force-activated alpha-helix swapping mechanism by which vinculin binding sites in talin rods are exposed works distinctly different from that of other force-activated bonds, including catch bonds.
Vesa P. Hytönen - One of the best experts on this subject based on the ideXlab platform.
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How force might activate talin's vinculin binding sites: SMD reveals a structural mechanism
PLoS Computational Biology, 2008Co-Authors: Vesa P. Hytönen, Viola VogelAbstract:Upon cell adhesion, talin physically couples the cytoskeleton via integrins to the extracellular matrix, and subsequent vinculin recruitment is enhanced by locally applied tensile force. Since the vinculin binding (VB) sites are buried in the talin rod under equilibrium conditions, the structural mechanism of how vinculin binding to talin is force-activated remains unknown. Taken together with experimental data, a biphasic vinculin binding model, as derived from steered molecular dynamics, provides high resolution structural insights how tensile mechanical force applied to the talin rod fragment (residues 486-889 constituting helices H1-H12) might activate the VB sites. Fragmentation of the rod into three helix Subbundles is prerequisite to the sequential exposure of VB helices to water. Finally, unfolding of a VB helix into a completely stretched polypeptide might inhibit further binding of vinculin. The first events in fracturing the H1-H12 rods of talin1 and talin2 in Subbundles are similar. The proposed force-activated alpha-helix swapping mechanism by which vinculin binding sites in talin rods are exposed works distinctly different from that of other force-activated bonds, including catch bonds.
Simion Filip - One of the best experts on this subject based on the ideXlab platform.
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Semisimplicity and rigidity of the Kontsevich-Zorich cocycle
Inventiones mathematicae, 2016Co-Authors: Simion FilipAbstract:We prove that invariant Subbundles of the Kontsevich-Zorich cocycle respect the Hodge structure. In particular, we establish a version of Deligne semisimplicity in this context. This implies that invariant Subbundles must vary polynomially on affine manifolds. All results apply to tensor powers of the cocycle and this implies that the measurable and real-analytic algebraic hulls coincide. We also prove that affine manifolds typically parametrize Jacobians with non-trivial endomorphisms. If the field of affine definition is larger than $$\mathbb {Q}$$ Q , then a factor has real multiplication. The tools involve curvature properties of the Hodge bundles and estimates from random walks. In the appendix, we explain how methods from ergodic theory imply some of the global consequences of Schmid’s work on variations of Hodge structures. We also derive the Kontsevich-Forni formula using differential geometry.
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semisimplicity and rigidity of the kontsevich zorich cocycle
arXiv: Dynamical Systems, 2013Co-Authors: Simion FilipAbstract:We prove that invariant Subbundles of the Kontsevich-Zorich cocycle respect the Hodge structure. In particular, we establish a version of Deligne semisimplicity in this context. This implies that invariant Subbundles must vary polynomially on affine manifolds. All results apply to tensor powers of the cocycle and this implies that the measurable and real-analytic algebraic hulls coincide. We also prove that affine manifolds parametrize Jacobians with non-trivial endomorphisms. Typically a factor has real multiplication. The tools involve curvature properties of the Hodge bundles and estimates from random walks. In the appendix, we explain how methods from ergodic theory imply some of the global consequences of Schmid's work on variations of Hodge structures. We also derive the Kontsevich-Forni formula using differential geometry.
