0000000000298186
AUTHOR
Manfred Lehn
showing 4 related works from this author
Generalized twisted cubics on a cubic fourfold as a moduli space of stable objects
2016
We revisit the work of Lehn-Lehn-Sorger-van Straten on twisted cubic curves in a cubic fourfold not containing a plane in terms of moduli spaces. We show that the blow-up $Z'$ along the cubic of the irreducible holomorphic symplectic eightfold $Z$, described by the four authors, is isomorphic to an irreducible component of a moduli space of Gieseker stable torsion sheaves or rank three torsion free sheaves. For a very general such cubic fourfold, we show that $Z$ is isomorphic to a connected component of a moduli space of tilt-stable objects in the derived category and to a moduli space of Bridgeland stable objects in the Kuznetsov component. Moreover, the contraction between $Z'$ and $Z$ i…
La singularité de O’Grady
2006
Let M 2 v M_{2v} be the moduli space of semistable sheaves with Mukai vector 2 v 2v on an abelian or K 3 K3 surface where v v is primitive such that ⟨ v , v ⟩ = 2 \langle v,v \rangle =2 . We show that the blow-up of the reduced singular locus of M 2 v M_{2v} provides a symplectic resolution of singularities. This provides a direct description of O’Grady’s resolutions of M K 3 ( 2 , 0 , 4 ) M_{K3}(2,0,4) and M A b ( 2 , 0 , 2 ) M_{Ab}(2,0,2) . Résumé. Soit M 2 v M_{2v} l’espace de modules des faisceaux semi-stables de vecteur de Mukai 2 v 2v sur une surface K 3 K3 ou abélienne où v v est primitif tel que ⟨ v , v ⟩ = 2 \langle v,v \rangle =2 . Nous montrons que l’éclatement de M 2 v M_{2v} le…
On the stability of flat complex vector bundles over parallelizable manifolds
2017
We investigate the flat holomorphic vector bundles over compact complex parallelizable manifolds $G / \Gamma$, where $G$ is a complex connected Lie group and $\Gamma$ is a cocompact lattice in it. The main result proved here is a structure theorem for flat holomorphic vector bundles $E_\rho$ associated to any irreducible representation $\rho : \Gamma \rightarrow \text{GL}(r,{\mathbb C})$. More precisely, we prove that $E_{\rho}$ is holomorphically isomorphic to a vector bundle of the form $E^{\oplus n}$, where $E$ is a stable vector bundle. All the rational Chern classes of $E$ vanish, in particular, its degree is zero. We deduce a stability result for flat holomorphic vector bundles $E_{\r…
The cup product of Hilbert schemes for K3 surfaces
2003
To any graded Frobenius algebra A we associate a sequence of graded Frobenius algebras A [n] so that there is canonical isomorphism of rings (H *(X;ℚ)[2]) [n] ≅H *(X [n] ;ℚ)[2n] for the Hilbert scheme X [n] of generalised n-tuples of any smooth projective surface X with numerically trivial canonical bundle.