Homotopy abelianity of the DG-Lie algebra controlling deformations of pairs (variety with trivial canonical bundle, line bundle)
نویسندگان
چکیده
We investigate the deformations of pairs [Formula: see text], where text] is a line bundle on smooth projective variety defined over an algebraically closed field characteristic 0. In particular, we prove that DG-Lie algebra controlling pair homotopy abelian whenever has trivial canonical bundle, and so these are unobstructed.
منابع مشابه
The Lie Algebra of Smooth Sections of a T-bundle
In this article, we generalize the concept of the Lie algebra of vector fields to the set of smooth sections of a T-bundle which is by definition a canonical generalization of the concept of a tangent bundle. We define a Lie bracket multiplication on this set so that it becomes a Lie algebra. In the particular case of tangent bundles this Lie algebra coincides with the Lie algebra of vector fie...
متن کاملHyperbolic geometry and non-Kähler manifolds with trivial canonical bundle
We use hyperbolic geometry to construct simply-connected symplectic or complex manifolds with trivial canonical bundle and with no compatible Kähler structure. We start with the desingularisations of the quadric cone in C: the smoothing is a natural S-bundle over H, its holomorphic geometry is determined by the hyperbolic metric; the small-resolution is a natural S-bundle over H with symplectic...
متن کاملHypercomplex manifolds with trivial canonical bundle and their holonomy
Let (M, I, J,K) be a compact hypercomplex manifold admitting a special kind of quaternionic-Hermitian metric called an HKT-metric. Assume that the canonical bundle of (M, I) is trivial as a holomorphic line bundle. We show that the holonomy of canonical torsion-free connection called Obata connection onM is contained in SL(n,H). In Appendix we apply these arguments to compact nilmanifolds which...
متن کاملDeformations of the Generalised Picard Bundle
Let X be a nonsingular algebraic curve of genus g ≥ 3, and let Mξ denote the moduli space of stable vector bundles of rank n ≥ 2 and degree d with fixed determinant ξ over X such that n and d are coprime. We assume that if g = 3 then n ≥ 4 and if g = 4 then n ≥ 3, and suppose further that n0, d0 are integers such that n0 ≥ 1 and nd0 + n0d > nn0(2g − 2). Let E be a semistable vector bundle over ...
متن کامل00 1 Deformations of the Picard Bundle
Let X be a nonsingular algebraic curve of genus g ≥ 3, and M ξ the moduli space of stable vector bundles of rank n ≥ 2 and degree d with fixed determinant ξ over X such that n and d coprime and d > n(2g − 2). We assume that if g = 3 then n ≥ 4 and if g = 4 then n ≥ 3. Let W ξ (L) denote the vector bundle over M ξ defined as the direct image π * (U ξ ⊗ p * 1 L) where U ξ is a universal vector bu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Mathematics
سال: 2021
ISSN: ['1793-6519', '0129-167X']
DOI: https://doi.org/10.1142/s0129167x21500865