共查询到20条相似文献,搜索用时 15 毫秒
1.
Yasunari Nagai 《Mathematische Zeitschrift》2008,258(2):407-426
We study the monodromy operators on the Betti cohomologies associated to a good degeneration of irreducible symplectic manifold
and we show that the unipotency of the monodromy operator on the middle cohomology is at least the half of the dimension.
This implies that the “mildest” singular fiber of a good degeneration with non-trivial monodromy of irreducible symplectic
manifolds is quite different from the generic degeneration of abelian varieties or Calabi–Yau manifolds. 相似文献
2.
3.
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
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5.
Jun-Muk Hwang 《Inventiones Mathematicae》2008,174(3):625-644
Given a projective irreducible symplectic manifold M of dimension 2n, a projective manifold X and a surjective holomorphic map f:M→X with connected fibers of positive dimension, we prove that X is biholomorphic to the projective space of dimension n. The proof is obtained by exploiting two geometric structures at general points of X: the affine structure arising from the action variables of the Lagrangian fibration f and the structure defined by the variety of minimal rational tangents on the Fano manifold X. 相似文献
6.
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
7.
Gianluca Occhetta 《manuscripta mathematica》2001,104(1):111-121
In this paper we classify pairs (X,ℰ) with ℰ ample vector bundle of rank r on a smooth variety X of dimension n= 2r−1 such that K
X
+ det ℰ=?
x
.
Received: 7 April 2000 相似文献
8.
Stefan Haller 《Advances in Mathematics》2003,180(1):87-103
Mathieu (Math. Helv. 70 (1995) 1) introduced a canonic filtration in the de Rham cohomology of a symplectic manifold and proved, that the middle filtration space is the space of harmonic cohomology classes. We give an interpretation of the other filtration spaces, prove a Künneth theorem for harmonic cohomology, prove Poincaré duality for harmonic cohomology and show how surjectivity of certain Lefschetz type mappings is related to properties of the filtration. For a closed symplectic manifold M we also introduce symplectic invariants , and show if M is of dimension 2n with n even. 相似文献
9.
Marco Andreatta 《Mathematische Zeitschrift》1999,230(4):713-726
Let X be a compact Moishezon manifold which becomes projective after blowing up a smooth subvariety . We assume also that there exists a proper map onto a projective variety with a point, such that and is -big. We prove some inequalities between the dimensions of Y andX and we construct examples which shows the optimality of the inequalities. In the last section we discuss some differential
geometry properties of these examples which lead to a conjecture.
Received December 19, 1997 相似文献
10.
Dominik Burek 《Mathematische Nachrichten》2020,293(4):638-650
Based on Cynk–Hulek method from [7] we construct complex Calabi–Yau varieties of arbitrary dimensions using elliptic curves with an automorphism of order 6. Also we give formulas for Hodge numbers of varieties obtained from that construction. We shall generalize the result of [11] to obtain arbitrarily dimensional Calabi–Yau manifolds which are Zariski in any characteristic . 相似文献
11.
We study the topology of the boundary manifold of a regular neighborhood of a complex projective hypersurface. We show that, under certain Hodge-theoretic conditions, the cohomology ring of the complement of the hypersurface functorially determines that of the boundary. When the hypersurface defines a hyperplane arrangement, the cohomology of the boundary is completely determined by the combinatorics of the underlying arrangement and the ambient dimension. We also study the LS category and topological complexity of the boundary manifold, as well as the resonance varieties of its cohomology ring. 相似文献
12.
《Mathematische Nachrichten》2017,290(8-9):1281-1302
By Jahnke–Peternell–Radloff and Takeuchi, almost Fano threefolds with del Pezzo fibrations were classified. Among them, there exist 10 classes such that the existence of members of these was not proved. In this paper, we construct such examples belonging to each of 10 classes. 相似文献
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14.
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
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18.
Linda Chen 《Advances in Mathematics》2003,174(1):1-34
We study two aspects of quantum Schubert calculus: a presentation of the (small) quantum cohomology ring of partial flag manifolds and a quantum Giambelli formula. Our proof gives a relationship between universal Schubert polynomials as defined by Fulton and quantum Schubert polynomials, as defined by Fomin, Gelfand, and Postnikov, and later extended by Ciocan-Fontanine. Intersection theory on hyperquot schemes is an essential element of the proof. 相似文献
19.
Andreas Leopold Knutsen 《Indagationes Mathematicae》2008,19(2):217-238
We give restrictions on the existence of families of curves on smooth projective surfaces S of nonnegative Kodaira dimension all having constant geometric genus pg ? 2 and hyperelliptic normalizations. In particular, we prove a Reider-like result that relies on deformation theory and bending-and-breaking of rational curves in Sym2(S). We also give examples of families of such curves. 相似文献
20.
Joseph A. Wolf 《Geometriae Dedicata》1995,57(1):111-120
The complete homogeneous pseudo-Riemannian manifolds of constant non-zero curvature were classified up to isometry in 1961 [1]. In the same year, a structure theory [2] was developed for complete flat homogeneous pseudo-Riemannian manifolds. Here that structure theory is sharpened to a classification. This completes the classification of complete homogeneous pseudo-Riemannian manifolds of arbitrary constant curvature.Research partially supported by N.S.F. Grant DMS 93 21285. 相似文献