共查询到20条相似文献,搜索用时 78 毫秒
1.
Peter Vermeire 《Journal of Pure and Applied Algebra》2007,211(3):622-632
We compute the expected dimension of the moduli space of torsion-free rank 2 sheaves at a point corresponding to a stable reflexive sheaf, and give conditions for the existence of a perfect tangent-obstruction complex on a class of smooth projective threefolds; this class includes Fano and Calabi-Yau threefolds. We also explore both local and global relationships between moduli spaces of reflexive rank 2 sheaves and the Hilbert scheme of curves. 相似文献
2.
Shizhuo Zhang 《Journal of Pure and Applied Algebra》2019,223(3):1139-1160
In this note we apply the techniques of the toric systems introduced by Hille–Perling to several problems on smooth projective surfaces: We showed that the existence of full exceptional collection of line bundles implies the rationality for small Picard rank surfaces; we proved equivalences of several notions of cyclic strong exceptional collection of line bundles; we also proposed a partial solution to a conjecture on exceptional sheaves on weak del Pezzo surfaces. 相似文献
3.
We systematically develop Bridgeland's [7] and Bridgeland–Maciocia's [10] techniques for studying elliptic fibrations, and identify criteria that ensure 2-term complexes are mapped to torsion-free sheaves under a Fourier–Mukai transform. As an application, we construct an open immersion from a moduli of stable complexes to a moduli of Gieseker stable sheaves on elliptic threefolds. As another application, we give various 1–1 correspondences between fibrewise semistable torsion-free sheaves and codimension-1 sheaves on Weierstrass surfaces. 相似文献
4.
We establish a—and conjecture further—relationship between the existence of subvarieties representing minimal cohomology classes
on principally polarized abelian varieties, and the generic vanishing of the cohomology of twisted ideal sheaves. The main
ingredient is the Generic Vanishing criterion established in Pareschi G. and Popa M. (GV-sheaves, Fourier–Mukai transform, and Generic Vanishing. Preprint math.AG/0608127), based on the Fourier–Mukai transform.
MP was partially supported by the NSF grant DMS 0500985 and by an AMS Centennial Fellowship. 相似文献
5.
Antony Maciocia 《Mathematische Nachrichten》2012,285(16):1981-1998
We study twisted ideal sheaves of small length on an irreducible principally polarized abelian surface $({\mathbb T},\ell )We study twisted ideal sheaves of small length on an irreducible principally polarized abelian surface $({\mathbb T},\ell )$. Using Fourier‐Mukai techniques we associate certain jumping schemes to such sheaves and completely classify such loci. We give examples of applications to the enumerative geometry of ${\mathbb T}$ and show that no smooth genus 5 curve on such a surface can contain a $g^1_3$. We also describe explicitly the singular divisors in the linear system |2?|. 相似文献
6.
Here we define the concept of Qregularity for coherent sheaves on a smooth quadric hypersurface Qn⊂Pn+1. In this setting we prove analogs of some classical properties. We compare the Qregularity of coherent sheaves on Qn with the Castelnuovo-Mumford regularity of their extension by zero in Pn+1. We also classify the coherent sheaves with Qregularity −∞. We use our notion of Qregularity in order to prove an extension of the Evans-Griffiths criterion to vector bundles on quadrics. In particular, we get a new and simple proof of Knörrer’s characterization of ACM bundles. 相似文献
7.
Kanetomo Sato 《Mathematische Zeitschrift》2007,257(4):707-743
In this paper, we define two kinds (homological and cohomological) of étale logarithmic Hodge–Witt sheaves on normal crossing
varieties over a perfect field of positive characteristic, and discuss some fundamental properties, in particular puity and
duality. 相似文献
8.
A quasi-coherent ringed scheme is a pair (X,
$$ \mathcal{A} $$), where X is a scheme, and
$$ \mathcal{A} $$
is a noncomutative quasi-coherent
$$ \mathcal{O}_X $$
-ring. We introduce dualizing complexes over quasi-coherent ringed schemes and study their properties. For a separated differential
quasi-coherent ringed scheme of finite type over a field, we prove existence and uniqueness of a rigid dualizing complex.
In the proof we use the theory of perverse coherent sheaves in order to glue local pieces of the rigid dualizing complex into
a global complex. 相似文献
9.
Markus Zowislok 《Mathematische Zeitschrift》2012,272(3-4):1195-1217
We investigate the moduli spaces of one- and two-dimensional sheaves on projective K3 and abelian surfaces that are semistable with respect to a nongeneral ample divisor with regard to the symplectic resolvability. We can exclude the existence of new examples of projective irreducible symplectic manifolds lying birationally over components of the moduli spaces of one-dimensional semistable sheaves on K3 surfaces, and over components of many of the moduli spaces of two-dimensional sheaves on K3 surfaces, in particular, of those for rank two sheaves. 相似文献
10.
Justin Sawon 《Advances in Mathematics》2008,218(3):828-864
We apply the methods of C a?ld?raru to construct a twisted Fourier-Mukai transform between a pair of holomorphic symplectic four-folds which are fibred by Lagrangian abelian surfaces. More precisely, we obtain an equivalence between the derived category of coherent sheaves on a certain Lagrangian fibration and the derived category of twisted sheaves on its ‘mirror’ partner. As a corollary, we extend the original Fourier-Mukai transform to degenerations of abelian surfaces. Another consequence of the general theory is that the holomorphic symplectic four-fold and its mirror are connected by a one-parameter family of deformations through Lagrangian fibrations. 相似文献
11.
Kōta Yoshioka 《Mathematische Annalen》2001,321(4):817-884
In this paper, we consider basic problems on moduli spaces of stable sheaves on abelian surfaces. Our main assumption is
the primitivity of the associated Mukai vector. We determine the deformation types, albanese maps, Bogomolov factors and their
weight 2 Hodge structures. We also discuss the deformation types of moduli spaces of stable sheaves on K3 surfaces.
Received: 28 February 2000 / Revised version: 15 September 2000 / Published online: 24 September 2001 相似文献
12.
Johannes Huisman 《Indagationes Mathematicae》2008,19(3):401-410
We prove, in an elementary way, that a locally free sheaf of finite rank over the anisotropic real conic is the direct sum of indecomposable locally free sheaves of rank 1 or 2. Our proof is purely algebraic, and is based on a classification of graded ?[X, Y]-modules endowed with a certain action of the cyclic group ?/4?. 相似文献
13.
We study relative Fourier–Mukai transforms on genus one fibrations with section, allowing explicitly the total space of the fibration to be singular and non-projective. Grothendieck duality is used to prove a skew–commutativity relation between this equivalence of categories and certain duality functors. We use our results to explicitly construct examples of semi-stable sheaves on degenerating families of elliptic curves. 相似文献
14.
Zhiwei Yun 《Selecta Mathematica, New Series》2009,14(2):299-320
We describe several general methods for calculating weights of mixed tilting sheaves. We introduce a notion called “non-cancellation
property” which implies a strong uniqueness of mixed tilting sheaves and enables one to calculate their weights effectively.
When we have a certain Radon transform, we prove a geometric analogue of Ringel duality which sends tilting objects to projective
objects. We apply these methods to (partial) flag varieties and affine (partial) flag varieties and show that the weight polynomials
of mixed tilting sheaves on flag and affine flag varieties are essentially given by Kazhdan-Lusztig polynomials. This verifies
a mixed geometric analogue of a conjecture by W. Soergel in [10].
相似文献
15.
For sheaves of differential forms of the de Rham–Witt complex for regular varieties over a perfect field of positive characteristic p we prove unconditional descent in cohomological dimension 0 with respect to Voevodsky's h-topology. Under resolution of singularities we obtain full cohomological descent. Our approach follows recent work of Huber–Jörder and Huber–Kebekus–Kelly on sheaves of differential forms. 相似文献
16.
We prove that a coherent DQ-kernel induces an equivalence between the derived categories of DQ-modules with coherent cohomology if and only if the graded commutative kernel associated to it induces an equivalence between the derived categories of coherent sheaves. 相似文献
17.
Shinnosuke Okawa 《Advances in Mathematics》2011,(5):2869
We show that the bounded derived category of coherent sheaves on a smooth projective curve except the projective line admits no non-trivial semi-orthogonal decompositions. 相似文献
18.
We define a notion of total acyclicity for complexes of flat quasi-coherent sheaves on a semi-separated noetherian scheme, and study these complexes using the pure derived category of flat quasi-coherent sheaves. We prove that a scheme is Gorenstein if and only if every acyclic complex of flat quasi-coherent sheaves is totally acyclic. Our formalism also removes the need for a dualising complex in several known results for rings, including Jørgensen's proof of the existence of Gorenstein projective precovers. 相似文献
19.
A quasi-coherent ringed scheme is a pair (X,
$$ \mathcal{A} $$), where X is a scheme, and
$$ \mathcal{A} $$
is a noncomutative quasi-coherent
$$ \mathcal{O}_X $$
-ring. We introduce dualizing complexes over quasi-coherent ringed schemes and study their properties. For a separated differential
quasi-coherent ringed scheme of finite type over a field, we prove existence and uniqueness of a rigid dualizing complex.
In the proof we use the theory of perverse coherent sheaves in order to glue local pieces of the rigid dualizing complex into
a global complex. 相似文献
20.
Shun-Ichi Kimura 《Inventiones Mathematicae》1999,137(3):575-611
Vistoli defined Alexander schemes in [19], which behave like smooth varieties from the viewpoint of intersection theory with
Q-coefficients. In this paper, we will affirmatively answer Vistoli’s conjecture that Alexander property is Zariski local.
The main tool is the abelian category of bivariant sheaves, and we will spend most of our time for proving basic properties
of this category. We show that a scheme is Alexander if and only if all the first cohomology groups of bivariant sheaves vanish,
which is an analogy of Serre’s theorem, which says that a scheme is affine if and only if all the first cohomology groups
of quasi-coherent sheaves vanish. Serre’s theorem implies that the union of affine closed subschemes is again affine. Mimicking
the proof line by line, we will prove that the union of Alexander open subschemes is again Alexander.
Oblatum 1-XII-1997 & 14-XII-1998 / Published online: 10 May 1999 相似文献