1,720,970 research outputs found
The second integral cohomology of moduli spaces of sheaves on K3 and Abelian surfaces
No full textIn this paper we study the second integral cohomology of moduli spaces of semistable sheaves on projective K3 surfaces. If S is a projective K3 surface, v a Mukai vector and H a polarization on S that is general with respect to v, we show that H2(Mv, Z) is a free Z -module of rank 23 carrying a pure weight -two Hodge structure and a lattice structure, with respect to which H2(Mv,Z) is Hodge isometric to the Hodge sublattice v perpendicular to of the Mukai lattice of S. Similar results are proved for Abelian surfaces. (c) 2024 Elsevier Inc. All rights reserved
Factoriality properties of moduli spaces of sheaves on abelian and K3 surfaces
No full textIn this paper, we complete the determination of the index of factoriality of moduli spaces of semistable sheaves on an abelian or projective K3 surface S. If v is a Mukai vector and H a generic polarization, let Mv(S,H) be the moduli space of H-semistable sheaves on S with Mukai vector v. First, we describe in terms of v the pure weight-2 Hodge structure and the Beauville form on the second integral cohomology of the symplectic resolutions of M v(S,H) (when S is K3) and of the fiber Kv(S,H) of the Albanese map of Mv(S,H) (when S is abelian). Then, if S is K3, we show that Mv(S,H) is either locally factorial or 2-factorial, and we give an example of both cases. If S is abelian, we show that Mv(S,H) and Kv(S,H) are 2-factorial
The 2-factoriality of the O'Grady moduli spaces
No full textThe aim of this work is to show that the moduli space M_{10} introduced by O'Grady is a 2-factorial variety. Namely, M_{10} is the moduli space of semistable sheaves with Mukai vector v:=(2,0,-2)\in H^{ev}(X,\mathbb{Z}) on a projective K3 surface X. As a corollary to our construction, we show that the Donaldson morphism gives a Hodge isometry between v (sublattice of the Mukai lattice of X) and its image in H^{2}(\widetilde{M}_{10},\mathbb{Z}), lattice with respect to the Beauville form of the 10-dimensional irreducible symplectic manifold \widetilde{M}_{10}, obtained as symplectic resolution of M_{10}. Similar results are shown for the moduli space M_{6} introduced by O'Grady to produce its 6-dimensional example of irreducible symplectic variety. © Springer-Verlag 2009
A Gabriel Theorem for Coherent Twisted Sheaves
No full text21 pages, Added referencesWe give a generalization of Gabriel's Theorem on coherent sheaves to the case of coherent twisted sheaves on a smooth variety X over a field k. We show that the category Coh(X,\alpha) determines the scheme structure of X for \alpha in the Brauer group of X, and that any equivalence between Coh(X,\alpha) and Coh(Y,\beta) induces an isomorphism between X and Y. In conclusion we prove the saturatedness of D^b(X,\alpha)
Locally trivial monodromy of moduli spaces of sheaves on K3 surfaces
No full textIn this paper we study monodromy operators on moduli spaces M-v (S, H) of sheaves on K3 surfaces with non-primitive Mukai vectors v. If we write v = mw , with m > 1 and w primitive, then our main result is that the inclusion M-w (S, H ) -> M-v (S, H ) as the most singular locus induces an isomorphism between the monodromy groups of these symplectic varieties, allowing us to extend to the non-primitive case a result of Markman
Deformation of the O'Grady moduli spaces
No full textIn this paper we study moduli spaces of sheaves on an abelian or projective K3 surface. If S is a K3, v = 2w is a Mukai vector on S, where w is primitive and w^{2}= 2, and H is a v-generic polarization on S, then the moduli space M_v of H-semistable sheaves on S whose Mukai vector is v admits a symplectic resolution \widetilde{M}_v. A particular case is the 10-dimensional O'Grady example \widetilde{M}_10 of an irreducible symplectic manifold. We show that \widetilde{M}_v is an irreducible symplectic manifold which is deformation equivalent to \widetilde{M}_10 and that H2(M_v,\mathbb{Z}) is Hodge isometric to the sublattice v^{\perp} of the Mukai lattice of S. Similar results are shown when S is an abelian surface. © Walter de Gruyter Berlin · Boston 2013
Moduli spaces of bundles over nonprojective K3 surfaces
No full textInternational audienceWe study moduli spaces of sheaves over nonprojective K3 surfaces. More precisely, let ω be a Kähler class on a K3 surface S, let r≥2 be an integer, and let v=(r,ξ,a) be a Mukai vector on S. We show that if the moduli space M of μω-stable vector bundles with associated Mukai vector v is compact, then M is an irreducible holomorphic symplectic manifold which is deformation equivalent to a Hilbert scheme of points on a K3 surface. Moreover, we show that there is a Hodge isometry between v⊥ and H2(M,ℤ) and that M is projective if and only if S is projective
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Kobayashi--Hitchin correspondence for twisted vector bundles
No full textWe prove the Kobayashi--Hitchin correspondence and the approximate Kobayashi--Hitchin correspondence for twisted holomorphic vector bundles on compact Kähler manifolds. More precisely, if X is a compact manifold and g is a Gauduchon metric on X, a twisted holomorphic vector bundle on X is
g−polystable if and only if it is g−Hermite-Einstein, and if X is a compact Kähler manifold and g is a Kähler metric on X, then a twisted holomorphic vector bundle on X is g−semistable if and only if it is approximate g−Hermite-Einstein
- …
