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《Mathematische Nachrichten》2017,290(5-6):876-884
We prove that the locus of Hilbert schemes of n points on a projective K 3 surface is dense in the moduli space of irreducible holomorphic symplectic manifolds of that deformation type. The analogous result for generalized Kummer manifolds is proven as well. Along the way we prove an integral constraint on the monodromy group of generalized Kummer manifolds. 相似文献
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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.
Oblatum 25-I-2001 & 18-IX-2002?Published online: 24 February 2003 相似文献
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L. Evain 《Transformation Groups》2007,12(2):227-249
Let X be a smooth projective toric surface, and
the Hilbert scheme parametrizing the length d zero-dimensional subschemes of X. We compute the rational Chow ring
. More precisely, if
is the two-dimensional torus contained in X, we compute the rational equivariant Chow ring
and the usual Chow ring is an explicit quotient of the equivariant Chow ring. The case of some quasi-projective toric surfaces
such as the affine plane are described by our method too. 相似文献
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We investigate the structure of the components of the moduli space of surfaces of general type, which parametrize surfaces
admitting nonsmooth genus 2 fibrations of nonalbanese type, over curves of genusg
b≥2. 相似文献
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Alberto Cattaneo 《Mathematische Nachrichten》2019,292(10):2137-2152
We study automorphisms of the Hilbert scheme of n points on a generic projective K3 surface S, for any . We show that is either trivial or generated by a non‐symplectic involution and we determine numerical and divisorial conditions which allow us to distinguish between the two cases. As an application of these results we prove that, for any , there exist infinitely many admissible degrees for the polarization of the K3 surface S such that admits a non‐natural involution. This provides a generalization of the results of [7] for . 相似文献
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A. Baragar 《Mathematische Annalen》1996,305(1):541-558
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Let X be a complex projective variety and consider the morphism
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JongHae Keum 《Journal of Pure and Applied Algebra》2019,223(4):1427-1433
In any characteristic p different from 2 and 5, Kondō gave an example of a K3 surface with a purely non-symplectic automorphism of order 50. The surface was explicitly given as a double plane branched along a smooth sextic curve. In this note we show that, in any characteristic , a K3 surface with a cyclic action of order 50 is isomorphic to the example of Kondō. 相似文献
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D.-Q. Zhang 《Journal of Pure and Applied Algebra》2006,207(1):119-138
In this note, we consider all possible extensions G of a non-trivial perfect group H acting faithfully on a K3 surface X. The pair (X,G) is proved to be uniquely determined by G if the transcendental value of G is maximum. In particular, we have , if H is the alternating group A5 and normal in G. 相似文献
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Let L be an ample line bundle on a K3 surface. We give a sharp bound on n for which nL is k-jet ample.Received: 27 December 2002 相似文献
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Fix a smooth very ample curve C on a K3 or abelian surface X. Let $ \mathcal{M} $ denote the
moduli space of pairs of the form (F, s), where F is a stable sheaf over X whose Hilbert polynomial
coincides with that of the direct image, by the inclusion map of C in X, of a line bundle of degree d
over C, and s is a nonzero section of F. Assume d to be sufficiently large such that F has a nonzero
section. The pullback of the Mukai symplectic form on moduli spaces of stable sheaves over X is
a holomorphic 2-form on $ \mathcal{M} $. On the other hand, $ \mathcal{M} $ has a map to a Hilbert scheme parametrizing
0-dimensional subschemes of X that sends (F, s) to the divisor, defined by s, on the curve defined
by the support of F. We prove that the above 2-form on $ \mathcal{M} $ coincides with the pullback of the
symplectic form on the Hilbert scheme. 相似文献
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In this paper we study K3 surfaces with a non-symplectic automorphism of order 3. In particular, we classify the topological
structure of the fixed locus of such automorphisms and we show that it determines the action on cohomology. This allows us
to describe the structure of the moduli space and to show that it has three irreducible components. 相似文献
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Matthias Schütt 《Archiv der Mathematik》2006,87(4):309-319
We prove that the maximal singular fibres of an elliptic K3 surface have type I19 and
unless the characteristic of the ground field is 2. In characteristic 2, the maximal singular fibres are I18 and
. The paper supplements work of Shioda in [9] and [10].
Received: 23 September 2005 相似文献
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Let Hc be the rational Cherednik algebra of type An-1 with spherical subalgebra Uc=eHce. Then Uc is filtered by order of differential operators, with associated graded ring where W is the nth symmetric group. We construct a filtered Z-algebra B such that, under mild conditions on c:• the category B-qgr of graded noetherian B-modules modulo torsion is equivalent to Uc-mod;• the associated graded Z-algebra has grB-lqgr?coh Hilb(n), the category of coherent sheaves on the Hilbert scheme of points in the plane.This can be regarded as saying that Uc simultaneously gives a non-commutative deformation of h⊕h*/W and of its resolution of singularities Hilb(n)→h⊕h*/W. As we show elsewhere, this result is a powerful tool for studying the representation theory of Hc and its relationship to Hilb(n). 相似文献
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Gülay Karadoğan-Kaya 《Archiv der Mathematik》2007,89(4):315-325
In this paper, we study the structure, deformations and the moduli spaces of complex projective surfaces admitting genus two
fibrations over elliptic curves. We observe that a surface admitting a smooth fibration as above is elliptic, and we employ
results on the moduli of polarized elliptic surfaces to construct moduli spaces of these smooth fibrations. In the case of
nonsmooth fibrations, we relate the moduli spaces to the Hurwitz schemes
of morphisms of degree n from elliptic curves to the modular curve X(d), d ≥ 3. Ultimately, we show that the moduli spaces in the nonsmooth case are fiber spaces over the affine line
with fibers determined by the components of
.
Received: 30 August 2006 相似文献