Canonical heights, invariant currents, and dynamical eigensystems of morphisms for line bundles

2006 ◽  
Vol 2006 (597) ◽  
Author(s):  
Shu Kawaguchi
Keyword(s):  
Line Bundles ◽  
Invariant Currents

scholarly journals Currents, charges and algebras in exceptional generalised geometry

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
David Osten
Keyword(s):  
Current Algebra ◽  
Hamiltonian Formulation ◽  
Building Blocks ◽  
Lie Derivative ◽  
Consistency Check ◽  
World Volume ◽  
Invariant Currents ◽  
Invariant Current ◽  
M Theory ◽  
A Current

Abstract A classical Ed(d)-invariant Hamiltonian formulation of world-volume theories of half-BPS p-branes in type IIb and eleven-dimensional supergravity is proposed, extending known results to d ≤ 6. It consists of a Hamiltonian, characterised by a generalised metric, and a current algebra constructed s.t. it reproduces the Ed(d) generalised Lie derivative. Ed(d)-covariance necessitates the introduction of so-called charges, specifying the type of p-brane and the choice of section. For p > 2, currents of p-branes are generically non- geometric due to the imposition of U-duality, e.g. the M5-currents contain coordinates associated to the M2-momentum.A derivation of the Ed(d)-invariant current algebra from a canonical Poisson structure is in general not possible. At most, one can derive a current algebra associated to para-Hermitian exceptional geometry.The membrane in the SL(5)-theory is studied in detail. It is shown that in a generalised frame the current algebra is twisted by the generalised fluxes. As a consistency check, the double dimensional reduction from membranes in M-theory to strings in type IIa string theory is performed. Many features generalise to p-branes in SL(p + 3) generalised geometries that form building blocks for the Ed(d)-invariant currents.

scholarly journals Higher rank Clifford indices of curves on a K3 surface

2021 ◽  
Vol 27 (3) ◽  
Author(s):  
Soheyla Feyzbakhsh ◽  
Chunyi Li
Keyword(s):  
Vector Bundles ◽  
Plane Curve ◽  
Smooth Curve ◽  
Line Bundles ◽  
K3 Surface ◽  
Clifford Index ◽  
Smooth Plane ◽  
Higher Rank ◽  
Rank Vector ◽  
Semistable Vector Bundle

AbstractLet (X, H) be a polarized K3 surface with $$\mathrm {Pic}(X) = \mathbb {Z}H$$ Pic ( X ) = Z H , and let $$C\in |H|$$ C ∈ | H | be a smooth curve of genus g. We give an upper bound on the dimension of global sections of a semistable vector bundle on C. This allows us to compute the higher rank Clifford indices of C with high genus. In particular, when $$g\ge r^2\ge 4$$ g ≥ r 2 ≥ 4 , the rank r Clifford index of C can be computed by the restriction of Lazarsfeld–Mukai bundles on X corresponding to line bundles on the curve C. This is a generalization of the result by Green and Lazarsfeld for curves on K3 surfaces to higher rank vector bundles. We also apply the same method to the projective plane and show that the rank r Clifford index of a degree $$d(\ge 5)$$ d ( ≥ 5 ) smooth plane curve is $$d-4$$ d - 4 , which is the same as the Clifford index of the curve.

scholarly journals Padé approximants on Riemann surfaces and KP tau functions

2021 ◽  
Vol 11 (4) ◽  
Author(s):  
Marco Bertola
Keyword(s):  
Riemann Surface ◽  
Riemann Surfaces ◽  
Hilbert Problem ◽  
Line Bundles ◽  
Fixed Degree ◽  
Tau Function ◽  
Tau Functions ◽  
Deformation Parameters ◽  
Higher Genus ◽  
Geometric Solutions

AbstractThe paper has two relatively distinct but connected goals; the first is to define the notion of Padé approximation of Weyl–Stiltjes transforms on an arbitrary compact Riemann surface of higher genus. The data consists of a contour in the Riemann surface and a measure on it, together with the additional datum of a local coordinate near a point and a divisor of degree g. The denominators of the resulting Padé-like approximation also satisfy an orthogonality relation and are sections of appropriate line bundles. A Riemann–Hilbert problem for a square matrix of rank two is shown to characterize these orthogonal sections, in a similar fashion to the ordinary orthogonal polynomial case. The second part extends this idea to explore its connection to integrable systems. The same data can be used to define a pairing between two sequences of line bundles. The locus in the deformation space where the pairing becomes degenerate for fixed degree coincides with the zeros of a “tau” function. We show how this tau function satisfies the Kadomtsev–Petviashvili hierarchy with respect to either deformation parameters, and a certain modification of the 2-Toda hierarchy when considering the whole sequence of tau functions. We also show how this construction is related to the Krichever construction of algebro-geometric solutions.

scholarly journals Topological Formulae for the Zeroth Cohomology of Line Bundles on del Pezzo and Hirzebruch Surfaces

2021 ◽  
Vol 8 (1) ◽  
pp. 223-229
Author(s):  
Callum R. Brodie ◽  
Andrei Constantin ◽  
Rehan Deen ◽  
Andre Lukas
Keyword(s):  
Topological Index ◽  
Line Bundles ◽  
Hirzebruch Surfaces ◽  
Del Pezzo

Abstract We show that the zeroth cohomology of effective line bundles on del Pezzo and Hirzebruch surfaces can always be computed in terms of a topological index.

Very ample line bundles on quasi-abelian varieties

2001 ◽  
Vol 236 (1) ◽  
pp. 191-200 ◽  
Author(s):  
Shigeharu Takayama
Keyword(s):  
Abelian Varieties ◽  
Line Bundles

scholarly journals Irreducible cone spherical metrics and stable extensions of two line bundles

2021 ◽  
Vol 388 ◽  
pp. 107854
Author(s):  
Lingguang Li ◽  
Jijian Song ◽  
Bin Xu
Keyword(s):  
Line Bundles

scholarly journals Approximation and equidistribution results for pseudo-effective line bundles

2018 ◽  
Vol 115 ◽  
pp. 218-236
Author(s):  
Dan Coman ◽  
George Marinescu ◽  
Viêt-Anh Nguyên
Keyword(s):  
Line Bundles

scholarly journals Cohomology of line bundles: Proof of the algorithm

2010 ◽  
Vol 51 (10) ◽  
pp. 103520 ◽  
Author(s):  
Helmut Roschy ◽  
Thorsten Rahn
Keyword(s):  
Line Bundles
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