1,720,974 research outputs found
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
Fine compactified Jacobians of reduced curves
No full textTo every singular reduced projective curve X one can associate many fine
compactified Jacobians, depending on the choice of a polarization on X, each of
which yields a modular compactification of a disjoint union of the generalized
Jacobian of X. We investigate the geometric properties of fine compactified
Jacobians focusing on curves having locally planar singularities. We give
examples of nodal curves admitting non isomorphic (and even non homeomorphic
over the field of complex numbers) fine compactified Jacobians. We study
universal fine compactified Jacobians, which are relative fine compactified
Jacobians over the semiuniversal deformation space of the curve X. Finally, we
investigate the existence of twisted Abel maps with values in suitable fine
compactified Jacobians
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
Monodromy and birational geometry of O'Grady's sixfolds
Full text linkWe prove that the bimeromorphic class of a hyperkähler manifold deformation equivalent to O’Grady’s six dimensional one is determined by the Hodge structure of its Beauville-Bogomolov lattice by showing that the monodromy group is maximal. As applications, we give the structure for the Kähler and the birational Kähler cones in this deformation class and we prove that the existence of a square zero divisor implies the existence a rational lagrangian fibration with fixed fibre types.We prove that the bimeromorphic class of a hyperkähler manifold deformation equivalent to O'Grady's six dimensional one is determined by the Hodge structure of its Beauville-Bogomolov lattice by showing that the monodromy group is maximal. As applications, we give the structure for the Kähler and the birational Kähler cones in this deformation class and we prove that the existence of a square zero divisor implies the existence a rational lagrangian fibration with fixed fibre types
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
The Hodge diamond of O’Grady’s six-dimensional example
Full text linkWe realize O’Grady’s six-dimensional example of an irreducible holomorphic symplectic (IHS) manifold as a quotient of an IHS manifold of K3 type by a birational involution, thereby computing its Hodge numbers
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
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
- …
