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1.
Let X be a normal Gorenstein complex projective variety. We introduce the Hilbert variety VX associated to the Hilbert polynomial χ(x1L1+?+xρLρ), where L1,…,Lρ is a basis of , ρ being the Picard number of X, and x1,…,xρ are complex variables. After studying general properties of VX we specialize to the Hilbert curve of a polarized variety (X,L), namely the plane curve of degree dim(X) associated to χ(xKX+yL). Special emphasis is given to the case of polarized threefolds. 相似文献
2.
3.
Let
be a very ample vector bundle of rank two on a smooth complex projective threefold X. An inequality about the third Segre class of
is provided when
is nef but not big, and when a suitable positive multiple of
defines a morphism X → B with connected fibers onto a smooth projective curve B, where KX is the canonical bundle of X. As an application, the case where the genus of B is positive and
has a global section whose zero locus is a smooth hyperelliptic curve of genus ≧ 2 is investigated, and our previous result
is improved for threefolds.
Received: 27 January 2005; revised: 26 March 2005 相似文献
4.
Working over , we show that, apart possibly from a unique limit point, the possible values of multi-point Seshadri constants for general points on smooth projective surfaces form a discrete set. In addition to its theoretical interest, this result is of practical value, which we demonstrate by giving significantly improved explicit lower bounds for Seshadri constants on and new results about ample divisors on blow ups of at general points. 相似文献
5.
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
6.
Dimitri Markushevich 《manuscripta mathematica》2006,120(2):131-150
A rational Lagrangian fibration f on an irreducible symplectic variety V is a rational map which is birationally equivalent to a regular surjective morphism with Lagrangian fibers. By analogy with K3 surfaces, it is natural to expect that a rational Lagrangian fibration exists if and only if V has a divisor D with Bogomolov–Beauville square 0. This conjecture is proved in the case when V is the Hilbert scheme of d points on a generic K3 surface S of genus g under the hypothesis that its degree 2g−2 is a square times 2d−2. The construction of f uses a twisted Fourier–Mukai transform which induces a birational isomorphism of V with a certain moduli space of twisted sheaves on another K3 surface M, obtained from S as its Fourier–Mukai partner. 相似文献
7.
Antonio Lanteri 《代数通讯》2013,41(12):5320-5329
8.
Eyal Markman 《Advances in Mathematics》2007,208(2):622-646
Let M be a smooth and compact moduli space of stable coherent sheaves on a projective surface S with an effective (or trivial) anti-canonical line bundle. We find generators for the cohomology ring of M, with integral coefficients. When S is simply connected and a universal sheaf E exists over S×M, then its class [E] admits a Künneth decomposition as a class in the tensor product of the topological K-rings. The generators are the Chern classes of the Künneth factors of [E] in . The general case is similar. 相似文献
9.
Indranil Biswas 《Journal of Pure and Applied Algebra》2008,212(10):2298-2306
We study certain moduli spaces of stable vector bundles of rank 2 on cubic and quartic threefolds. In many cases under consideration, it turns out that the moduli space is complete and irreducible and a general member has vanishing intermediate cohomology. In one case, all except one component of the moduli space has such vector bundles. 相似文献
10.
LetC be a smooth curve with ag
n
1
, i.e. a linear system of dimension 1 and degreen, lying on a smooth projective surfaceS. Let :S P
N
be the map associated to the line bundleK
S
+[C] and letD be a general divisor of the given linear systemg
n
1
. LetV be the linear space spanned by the image ofD through . We study the case in whichn:=dimV=1 and in general we discuss the case in whichn is small. The starting point is an analysis of the adjunction map using Bogomolov-Reider-Serrano techniques; several results from curve theory are also needed. 相似文献
11.
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
12.
J. Keum 《Journal of Pure and Applied Algebra》2002,170(1):67-91
We investigate when the fundamental group of the smooth part of a K3 surface or Enriques surface with Du Val singularities, is finite. As a corollary we give an effective upper bound for the order of the fundamental group of the smooth part of a certain Fano 3-fold. This result supports Conjecture A below, while Conjecture A (or alternatively the rational-connectedness conjecture in Kollar et al. (J. Algebra Geom. 1 (1992) 429) which is still open when the dimension is at least 4) would imply that every log terminal Fano variety has a finite fundamental group. 相似文献
13.
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
14.
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
15.
Yoshiaki Fukuma 《Journal of Pure and Applied Algebra》2007,209(1):99-117
Let (X,L) be a polarized manifold of dimension n. In this paper, for any integer i with 0≤i≤n we introduce the notion of the ith sectional invariant of (X,L). We define the ith sectional Euler number ei(X,L), the ith sectional Betti number bi(X,L), and the ith sectional Hodge number of type (j,i−j) of (X,L) and we will study some properties of these. 相似文献
16.
Yoshiaki Fukuma 《Journal of Pure and Applied Algebra》2011,215(2):168-184
Let X be a smooth complex projective variety of dimension 3 and let L be an ample line bundle on X. In this paper, we provide a lower bound for h0(m(KX+L)) under the assumption that κ(KX+L)≥0. In particular, we get the following: (1) if 0≤κ(KX+L)≤2, then h0(KX+L)>0 holds. (2) If κ(KX+L)=3, then h0(2(KX+L))≥3 holds. Moreover we get a classification of (X,L) with κ(KX+L)=3 and h0(2(KX+L))=3 or 4. 相似文献
17.
Let X be a smooth complex projective variety and let
be
a smooth submanifold of dimension
, which is the zero
locus of a section of an ample vector bundle
of rank
on X. Let H be an ample line bundle
on X, whose restriction
HZ to Z is generated by global sections.
Triplets
as above are classified under the
assumption that
is a polarized manifold of sectional genus
2. This can be regarded as a step towards the classification of ample
vector bundles of corank one and curve genus two.
Received: 6 June 2003 相似文献
18.
Benjamin E. Diamond 《Journal of Pure and Applied Algebra》2018,222(5):1164-1188
According to a conjecture attributed to Hartshorne and Lichtenbaum and proven by Ellingsrud and Peskine [18], the smooth rational surfaces in belong to only finitely many families. We formulate and study a collection of analogous problems in which is replaced by a smooth fourfold X with vanishing first integral Chern class. We embed such X into a smooth ambient variety and count families of smooth surfaces which arise in X from the ambient variety. We obtain various finiteness results in such settings. The central technique is the introduction of a new numerical invariant for smooth surfaces in smooth fourfolds with vanishing first Chern class. 相似文献
19.
Yoshiaki Fukuma 《Journal of Pure and Applied Algebra》2007,211(3):609-621
Let (X,L) be a polarized manifold of dimension n defined over the field of complex numbers. In this paper, we treat the case where n=3 and 4. First we study the case of n=3 and we give an explicit lower bound for h0(KX+L) if κ(X)≥0. Moreover, we show the following: if κ(KX+L)≥0, then h0(KX+L)>0 unless κ(X)=−∞ and h1(OX)=0. This gives us a partial answer of Effective Non-vanishing Conjecture for polarized 3-folds. Next for n=4 we investigate the dimension of H0(KX+mL) for m≥2. If n=4 and κ(X)≥0, then a lower bound for h0(KX+mL) is obtained. We also consider a conjecture of Beltrametti-Sommese for 4-folds and we can prove that this conjecture is true unless κ(X)=−∞ and h1(OX)=0. Furthermore we prove the following: if (X,L) is a polarized 4-fold with κ(X)≥0 and h1(OX)>0, then h0(KX+L)>0. 相似文献
20.
Stable surfaces and their log analogues are the type of varieties naturally occurring as boundary points in moduli spaces. We extend classical results of Kodaira and Bombieri to this more general setting: if (X,Δ) is a stable log surface with reduced boundary (possibly empty) and I is its global index, then 4I(KX+Δ) is base-point-free and 8I(KX+Δ) is very ample. 相似文献