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Cohomology Groups of Deformations of Line Bundles on Complex Tori  [PDF]
O. Ben-Bassat,N. Solomon
Mathematics , 2009, DOI: 10.1007/s11856-011-0143-0
Abstract: The cohomology groups of line bundles over complex tori (or abelian varieties) are classically studied invariants of these spaces. In this article, we compute the cohomology groups of line bundles over various holomorphic, non-commutative deformations of complex tori. Our analysis interpolates between two extreme cases. The first case is a calculation of the space of (cohomological) theta functions for line bundles over constant, commutative deformations. The second case is a calculation of the cohomologies of non-commutative deformations of degree-zero line bundles.
Automorphisms of moduli spaces of vector bundles over a curve  [PDF]
Indranil Biswas,Tomas L. Gomez,V. Munoz
Mathematics , 2012,
Abstract: Let X be an irreducible smooth complex projective curve of genus g at least 4. Let M(r,\Lambda) be the moduli space of stable vector bundles over X or rank r and fixed determinant \Lambda, of degree d. We give a new proof of the fact that the automorphism group of M(r,\Lambda) is generated by automorphisms of the curve X, tensorization with suitable line bundles, and, if r divides 2d, also dualization of vector bundles.
Line bundles on complex tori and a conjecture of Kodaira  [PDF]
Jean-Pierre Demailly,Thomas Eckl,Thomas Peternell
Mathematics , 2002,
Abstract: A famous conjecture attributed to Kodaira asks whether any compact Kaehler manifold can be approximated by projective manifolds. We confirm this conjecture on projectivized direct sums of three line bundles on three-dimensional complex tori which appears rather surprising in view of expected dimensions of certain families of tori. We also discuss possible counter examples.
Endotrivial representations of finite groups and equivariant line bundles on the Brown complex  [PDF]
Paul Balmer
Mathematics , 2015,
Abstract: We relate endotrivial representations of a finite group in characteristic p to equivariant line bundles on the simplicial complex of non-trivial p-subgroups, by means of weak homomorphisms.
Complex Line Bundles over Simplicial Complexes and their Applications  [PDF]
Felix Kn?ppel,Ulrich Pinkall
Computer Science , 2015,
Abstract: Discrete vector bundles are important in Physics and recently found remarkable applications in Computer Graphics. This article approaches discrete bundles from the viewpoint of Discrete Differential Geometry, including a complete classification of discrete vector bundles over finite simplicial complexes. In particular, we obtain a discrete analogue of a theorem of Andr\'e Weil on the classification of hermitian line bundles. Moreover, we associate to each discrete hermitian line bundle with curvature a unique piecewise-smooth hermitian line bundle of piecewise constant curvature. This is then used to define a discrete Dirichlet energy which generalizes the well-known cotangent Laplace operator to discrete hermitian line bundles over Euclidean simplicial manifolds of arbitrary dimension.
Automorphisms of moduli spaces of symplectic bundle  [PDF]
Indranil Biswas,Tomas L. Gomez,Vicente Mu?oz
Mathematics , 2010,
Abstract: Let X be an irreducible smooth complex projective curve of genus at least 3. Fix a line bundle L on X. Let M_{Sp}(L) be the moduli space of symplectic bundles (E, ExE ---> L) on X, with the symplectic form taking values in L. We show that the automorphism group of M_{Sp}(L) is generated by automorphisms sending E to ExM, where M is a 2-torsion line bundle, and automorphisms induced by automorphisms of X.
Categories of holomorphic line bundles on higher dimensional noncommutative complex tori  [PDF]
Hiroshige Kajiura
Mathematics , 2005, DOI: 10.1063/1.2719564
Abstract: We construct explicitly noncommutative deformations of categories of holomorphic line bundles over higher dimensional tori. Our basic tools are Heisenberg modules over noncommutative tori and complex/holomorphic structures on them introduced by A. Schwarz. We obtain differential graded (DG) categories as full subcategories of curved DG categories of Heisenberg modules over the complex noncommutative tori. Also, we present the explicit composition formula of morphisms, which in fact depends on the noncommutativity.
Steady Ricci Solitons on Complex Line Bundles  [PDF]
Maxwell Stolarski
Mathematics , 2015,
Abstract: We show the existence and uniqueness of a one-parameter family of smooth complete $U(1)$-invariant gradient steady Ricci solitons on the total space of any complex line bundle over a Fano K\"ahler-Einstein base with first Chern class proportional to that of the base. These solitons are non-K\"ahler except in the case that the first Chern classes are equal, and so we obtain new examples of non-K\"ahler Ricci solitons.
A Characterization of Complex Projective Spaces by Sections of Line Bundles  [PDF]
Shuyu Liang, Yanan Gao, Yicai Zhao
Advances in Pure Mathematics (APM) , 2015, DOI: 10.4236/apm.2015.58044
Abstract: Let M be a n-dimensional compact irreducible complex space with a line bundle L. It is shown that if M is completely intersected with respect to L and dimH0(M, L) = n + 1, then M is biholomorphic to a complex projective space Pn of dimension n.
Calabi-Yau Manifolds of Cohomogeneity One as Complex Line Bundles  [PDF]
Kiyoshi Higashijima,Tetsuji Kimura,Muneto Nitta
Mathematics , 2002, DOI: 10.1016/S0550-3213(02)00750-2
Abstract: We present a simple derivation of the Ricci-flat Kahler metric and its Kahler potential on the canonical line bundle over arbitrary Kahler coset space equipped with the Kahler-Einstein metric.
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