Der Satz von Grauert-Mülich für beliebige semistabile holomorphe Vektorbündel über dem n-dimensionalen komplex-projektiven Raum.
Derived categories of coherent sheaves on rational homogeneous manifolds.
Derived category of toric varieties with small Picard number
This paper aims to construct a full strongly exceptional collection of line bundles in the derived category D b(X), where X is the blow up of ℙn−r ×ℙr along a multilinear subspace ℙn−r−1×ℙr−1 of codimension 2 of ℙn−r ×ℙr. As a main tool we use the splitting of the Frobenius direct image of line bundles on toric varieties.
Derived invariance of the number of holomorphic -forms and vector fields
We prove that smooth projective varieties with equivalent derived categories have isogenous Picard varieties. In particular their irregularity and number of independent vector fields are the same. This implies that all Hodge numbers are the same for arbitrary derived equivalent threefolds, as well as other consequences of derived equivalence based on numerical criteria.
Des fibrés globalement engendrés sur l' espace projectif.
Des fibrés uniformes non homogènes.
Des fibrés uniformes non homogènes et indécomposables de rang (2n + 1) sur Pn ( C ), n ... 3.
Determinantal Barlow surfaces and phantom categories
We prove that the bounded derived category of the surface constructed by Barlow admits a length 11 exceptional sequence consisting of (explicit) line bundles. Moreover, we show that in a small neighbourhood of in the moduli space of determinantal Barlow surfaces, the generic surface has a semiorthogonal decomposition of its derived category into a length 11 exceptional sequence of line bundles and a category with trivial Grothendieck group and Hochschild homology, called a phantom category....
Determining obstructions for space curves, with applications to non-reduced components of the Hilbert scheme.
Die Modulräume 3MstIP3 (?2,3,c3) .
Diffeomorphism types of elliptic surfaces with pg=1.
Differential graded Lie algebras controlling infinitesimal deformations of coherent sheaves
Direct Images of Sheaves of Differentials and the Atiyah Class.
Droites des saut des fibrés stables de rang élevé sur IP2.
d-Very-Ample Line Bundles and embeddings of Hilbert Schemes of 0-cycles.
Dynamics in the moduli space of Abelian differentials.
Effective bounds for semipositive sheaves and for the height of points on curves over complex function fields
Ein ?Descente"-Lemma und Grothendiecks Projektionssatz für nicht-noethersche Schemata.
Ein Kriterium für vollständige Durchschnitte.
Ein Satz über die Einschränkung holomorpher Vektorbündel auf Pn mit c1 = 0 auf Hyperebenen.