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1.
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
2.
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
3.
D. Markushevich 《Mathematische Annalen》2008,342(1):145-156
Given a K3 surface S, we show that the relative intermediate Jacobian of the universal family of Fano 3-folds V containing S as an anticanonical divisor is a Lagrangian fibration. 相似文献
4.
C. G. Madonna 《Monatshefte für Mathematik》2005,146(4):333-339
We give infinitely many examples in which the moduli space of rank 2 H-stable sheaves on a K3 surface S endowed by a polarization H of degree 2g – 2, with Chern classes c1 = H and c2 = g – 1, is birationally equivalent to the Hilbert scheme S[g – 4] of zero dimensional subschemes of S of length g – 4. We get in this way a partial generalization of results from [5] and [1]. 相似文献
5.
For a general K3 surface S of genus g, with 2 ≤ g ≤ 10, we prove that the intermediate Jacobians of the family of prime Fano threefolds of genus g containing S as a hyperplane section, form generically an algebraic completely integrable Hamiltonian system.
The first author is partially supported by grant MI1503/2005 of the Bulgarian Foundation for Scientific Research. 相似文献
6.
Jin-Xing Cai 《manuscripta mathematica》1998,95(1):273-287
LetX, Y be smooth complex projective varieties, andf: X →Y be a fiber space whose general fiber is a curve of genusg. Denote byq
f
the relative irregularity off. It is proved thatq
f
≤5g+1 / 6, iff is not generically trivial; moreover, if either a)f is non-constant and the general fiber is either hyperelliptic or bielliptic or b)q(Y)=0, thenq
f
≤g+1 / 2, and the bound is best possible.
A classification of fiber surfaces of genus 3 withq
f
=2 is also given in this note.
Project supported by China Postdoctoral Science Foundation 相似文献
7.
In this paper we study 16 complete intersection K3-fibered Calabi--Yau variety types in biprojective space ℙ
n
1}×ℙ1. These are all the CICY-types that are K3 fibered by the projection on the second factor. We prove existence of isolated rational curves of bidegree (d,0) for every positive integer d on a general Calabi–Yau variety of these types. The proof depends heavily on existence theorems for curves on K3-surfaces proved by S. Mori and K. Oguiso. Some of these varieties are related to Calabi–Yau varieties in projective space
by a determinantal contraction, and we use this to prove existence of rational curves of every degree for a general Calabi–Yau
variety in projective space.
Received: 14 October 1997 / Revised version: 18 January 1998 相似文献
8.
9.
Let S be a smooth projective surface over C polarized by a 2-very ample line bundle L=O
S(L), i.e. for any 0-dimensional subscheme (Z,O
Z
) of length 3 the restriction map Γ(L)→Γ(L⊗O
Z) is a surjection. This generalization of very ampleness was recently introduced by M. Beltrametti and A.J. Sommese.
The authors prove that, if L·L≥13, the adjoint line bundleK
S⊗L is 2-very ample apart from a list of well understood exceptions and up to contracting down the smooth rational curves E such
that E·E=−1, L·E=2.
The appendix contains an inductive argument in order to extend the result in higher dimension. 相似文献
10.
F. Bottacin 《manuscripta mathematica》1998,97(4):517-527
In this paper we prove that if S is a Poisson surface, i.e., a smooth algebraic surface with a Poisson structure, the Hilbert scheme of points of S has a natural Poisson structure, induced by the one of S. This generalizes previous results obtained by A. Beauville [B1] and S. Mukai [M2] in the symplectic case, i.e., when S is an abelian or K3 surface. Finally we apply our results to give some examples of integrable Hamiltonian systems naturally
defined on these Hilbert schemes. In the simple case S=ℙ2 we obtain by this construction a large class of integrable systems, which includes the ones studied by P. Vanhaecke in [V1]
and, more generally, in [V2].
Received: 9 March 1998 / Revised version: 19 June 1998 相似文献
11.
《Selecta Mathematica, New Series》2005,11(3-4):399-451
We verify the conjecture formulated in [36] for suspension singularities of type g(x, y, z)=f(x, y)+zn, where f is an irreducible plane curve singularity. More precisely, we prove that the modified Seiberg–Witten invariant of the link
M of g, associated with the canonical spinc structure, equals −σ(F)/8, where σ(F) is the signature of the Milnor fiber of g. In order to do this, we prove general splicing formulae for the Casson–Walker invariant and for the sign-refined Reidemeister–Turaev
torsion. These provide results for some cyclic covers as well. As a by-product, we compute all the relevant invariants of
M in terms of the Newton pairs of f and the integer n. 相似文献
12.
13.
In this paper we investigate a certain linear combination K([(x)\vec])=K(a;b,c,d;e,f,g)K(\vec{x})=K(a;b,c,d;e,f,g) of two Saalschutzian hypergeometric series of type 4
F
3(1). We first show that K([(x)\vec])K(\vec{x}) is invariant under the action of a certain matrix group G
K
, isomorphic to the symmetric group S
6, acting on the affine hyperplane V={(a,b,c,d,e,f,g)∈ℂ7:e+f+g−a−b−c−d=1}. We further develop an algebra of three-term relations for K(a;b,c,d;e,f,g). We show that, for any three elements μ
1,μ
2,μ
3 of a certain matrix group M
K
, isomorphic to the Coxeter group W(D
6) (of order 23040) and containing the above group G
K
, there is a relation among K(m1[(x)\vec])K(\mu_{1}\vec{x}), K(m2[(x)\vec])K(\mu_{2}\vec{x}), and K(m3[(x)\vec])K(\mu_{3}\vec{x}), provided that no two of the μ
j
’s are in the same right coset of G
K
in M
K
. The coefficients in these three-term relations are seen to be rational combinations of gamma and sine functions in a,b,c,d,e,f,g. 相似文献
14.
How Close to Regular Must a Semicomplete Multipartite Digraph Be to Secure Hamiltonicity? 总被引:1,自引:0,他引:1
Anders Yeo 《Graphs and Combinatorics》1999,15(4):481-493
Let D be a semicomplete multipartite digraph, with partite sets V
1, V
2,…, V
c, such that |V
1|≤|V
2|≤…≤|V
c|. Define f(D)=|V(D)|−3|V
c|+1 and . We define the irregularity i(D) of D to be max|d
+(x)−d
−(y)| over all vertices x and y of D (possibly x=y). We define the local irregularity i
l(D) of D to be max|d
+(x)−d
−(x)| over all vertices x of D and we define the global irregularity of D to be i
g(D)=max{d
+(x),d
−(x) : x∈V(D)}−min{d
+(y),d
−(y) : y∈V(D)}. In this paper we show that if i
g(D)≤g(D) or if i
l(D)≤min{f(D), g(D)} then D is Hamiltonian. We furthermore show how this implies a theorem which generalizes two results by Volkmann and solves a stated
problem and a conjecture from [6]. Our result also gives support to the conjecture from [6] that all diregular c-partite tournaments (c≥4) are pancyclic, and it is used in [9], which proves this conjecture for all c≥5. Finally we show that our result in some sense is best possible, by giving an infinite class of non-Hamiltonian semicomplete
multipartite digraphs, D, with i
g(D)=i(D)=i
l(D)=g(D)+?≤f(D)+1.
Revised: September 17, 1998 相似文献
15.
Some years ago Caporaso and Harris have found a nice way to compute the numbers N(d, g) of complex plane curves of degree d and genus g through 3d + g − 1 general points with the help of relative Gromov-Witten invariants. Recently, Mikhalkin has found a way to reinterpret
the numbers N(d, g) in terms of tropical geometry and to compute them by counting certain lattice paths in integral polytopes. We relate these
two results by defining an analogue of the relative Gromov-Witten invariants and rederiving the Caporaso–Harris formula in
terms of both tropical geometry and lattice paths.
H. Markwig has been funded by the DFG grant Ga 636/2. 相似文献
16.
Timothy Logvinenko 《Mathematische Annalen》2008,341(1):137-167
In most cases where it has been shown to exist the derived McKay correspondence can be written as a Fourier–Mukai transform which sends point sheaves of the crepant resolution Y to pure sheaves in . We give a sufficient condition for to be the defining object of such a transform. We use it to construct the first example of the derived McKay correspondence
for a non-projective crepant resolution of . Along the way we extract more geometrical meaning out of the Intersection Theorem and learn to compute θ-stable families of G-constellations and their direct transforms. 相似文献
17.
Toufik Zaimi 《Archiv der Mathematik》2006,87(2):124-128
Let N be a positive rational integer and let P be the set of powers of a Salem number of degree d. We prove that for any α∈P the fractional parts of the numbers
, when n runs through the set of positive rational integers, are dense in the unit interval if and only if N≦ 2d − 4. We also show that for any α∈P the integer parts of the numbers αn are divisible by N for infinitely many n if and only if N≦ 2d − 3.
Received: 27 April 2005 相似文献
18.
Edoardo Ballico 《Results in Mathematics》2007,50(3-4):169-172
Fix non-negative integers r, e, m, g, s such that r ≥ 3, 0 ≤ m < r, e > 0, g + s ≤ er + max{0, m − 1} + 2, g ≤ (e − 1)r + max{0,m − 1} and 0 ≤ s ≤ er + 2. Set d := er + m. Fix any such that and S is in linearly general position. Fix an ordering of the points P
1, . . . , P
s
of S. Here we prove the existence of an irreducible family Γ of smooth, non-degenerate and connected curves with degree d and genus g, all of them containing S and such that the induced map is dominant.
Received: September 19, 2006. 相似文献
19.
A. L. Myl’nikov 《Algebra and Logic》2007,46(4):250-262
A subset K of a group G is said to be twisted if 1 ∈ K and xy−1x ∈ K for any x, y ∈ K. We explore finite twisted subsets with involutions which are themselves not subgroups but every proper
twisted subset of which is. Groups that are generated by such twisted subsets are classified.
__________
Translated from Algebra i Logika, Vol. 46, No. 4, pp. 459–482, July–August, 2007. 相似文献
20.
Ravi Vakil 《manuscripta mathematica》2000,102(1):53-84
In [CH3], Caporaso and Harris derive recursive formulas counting nodal plane curves of degree d and geometric genus g in the plane (through the appropriate number of fixed general points). We rephrase their arguments in the language of maps,
and extend them to other rational surfaces, and other specified intersections with a divisor. As applications, (i) we count
irreducible curves on Hirzebruch surfaces in a fixed divisor class and of fixed geometric genus, (ii) we compute the higher-genus
Gromov–Witten invariants of (or equivalently, counting curves of any genus and divisor class on) del Pezzo surfaces of degree
at least 3. In the case of the cubic surface in (ii), we first use a result of Graber to enumeratively interpret higher-genus
Gromov–Witten invariants of certain K-nef surfaces, and then apply this to a degeneration of a cubic surface.
Received: 30 June 1999 / Revised version: 1 January 2000 相似文献