Results 1 to 10 of about 249 (40)

Smoothing toroidal crossing spaces

Forum of Mathematics, Pi, 2021
We prove the existence of a smoothing for a toroidal crossing space under mild assumptions. By linking log structures with infinitesimal deformations, the result receives a very compact form for normal crossing spaces.
Simon Felten, Matej Filip, Helge Ruddat
doaj   +1 more source

Abelian Complex Structures and Generalizations

Complex Manifolds, 2021
After a review on the development of deformation theory of abelian complex structures from both the classical and generalized sense, we propose the concept of semi-abelian generalized complex structure.
Poon Yat Sun
doaj   +1 more source

Nodal curves with general moduli on K3 surfaces [PDF]

, 2007
We investigate the modular properties of nodal curves on a low genus K3 surface. We prove that a general genus g curve C is the normalization of a d-nodal curve X sitting on a primitively polarized K3 surface S of degree 2p-2, for p any integer between 3
Flamini, Flaminio, Knutsen, Andreas L., Pacienza, Gianluca, Sernesi, Edoardo   +3 more
core   +2 more sources

Global Geometric Deformations of the Virasoro algebra, current and affine algebras by Krichever-Novikov type algebra [PDF]

, 2006
In two earlier articles we constructed algebraic-geometric families of genus one (i.e. elliptic) Lie algebras of Krichever-Novikov type. The considered algebras are vector fields, current and affine Lie algebras.
A. Fialowski, A. Fialowski, A. Fialowski, A. Fialowski, A. Fialowski, A. Fialowski, A. Nijenhuis, A. Nijenhuis, A. Tsuchiya, A.A. Belavin, H. Bjar, I.M. Krichever, I.M. Krichever, I.M. Krichever, M. Gerstenhaber, M. Gerstenhaber, M. Gerstenhaber, M. Schlichenmaier, M. Schlichenmaier, M. Schlichenmaier, M. Schlichenmaier, M. Schlichenmaier, M. Schlichenmaier, M. Schlichenmaier, M. Schlichenmaier, M. Schlichenmaier, M. Schlichenmaier, M. Schlichenmaier, P. Lecomte, V.P. Palamodov   +29 more
core   +2 more sources

Which weakly ramified group actions admit a universal formal deformation? [PDF]

, 2008
Consider a formal (mixed-characteristic) deformation functor D of a representation of a finite group G as automorphisms of a power series ring k[[t]] over a perfect field k of positive characteristic. Assume that the action of G is weakly ramified, i.e.,
Byszewski, Jakub, Cornelissen, Gunther
core   +3 more sources

Contractions and deformations [PDF]

, 2018
Suppose that f is a projective birational morphism with at most one-dimensional fibres between d-dimensional varieties X and Y, satisfying ${\bf R}f_* \mathcal{O}_X = \mathcal{O}_Y$. Consider the locus L in Y over which f is not an isomorphism.
Donovan, Will, Wemyss, Michael
core   +2 more sources

Normal bundles to Laufer rational curves in local Calabi-Yau threefolds

, 2005
We prove a conjecture by F. Ferrari. Let X be the total space of a nonlinear deformation of a rank 2 holomorphic vector bundle on a smooth rational curve, such that X has trivial canonical bundle and has sections.
Bruzzo, U., Ricco, A.
core   +1 more source

Deformations of Calabi–Yau varieties with k-liminal singularities

Forum of Mathematics, Sigma
The goal of this paper is to describe certain nonlinear topological obstructions for the existence of first-order smoothings of mildly singular Calabi–Yau varieties of dimension at least $4$ .
Robert Friedman, Radu Laza
doaj   +1 more source

Leibniz algebra deformations of a Lie algebra

, 2008
In this note we compute Leibniz algebra deformations of the 3-dimensional nilpotent Lie algebra $\mathfrak{n}_3$ and compare it with its Lie deformations. It turns out that there are 3 extra Leibniz deformations.
Alice Fialowski, Ashis Mandal, Fialowski A., Fialowski A., Loday J.-L., Loday J.-L.   +5 more
core   +2 more sources

Smoothing, scattering and a conjecture of Fukaya

Forum of Mathematics, Pi
In 2002, Fukaya [19] proposed a remarkable explanation of mirror symmetry detailing the Strominger–Yau–Zaslow (SYZ) conjecture [47] by introducing two correspondences: one between the theory of pseudo-holomorphic curves on a Calabi–Yau manifold ...
Kwokwai Chan, Naichung Conan Leung, Ziming Nikolas Ma   +2 more
doaj   +1 more source