共查询到20条相似文献,搜索用时 237 毫秒
1.
Fumiharu Kato 《Mathematische Zeitschrift》2008,259(3):631-641
We give an explicit construction of a unitary Shimura surface that has Mumford’s fake projective plane as one of its connected
components. Moreover, as a byproduct of the construction, we show that Mumford’s fake projective place has a model defined
over the 7th cyclotomic field. 相似文献
2.
We conjecture that derived categories of coherent sheaves on fake projective n -spaces have a semi-orthogonal decomposition into a collection of n+1 exceptional objects and a category with vanishing Hochschild homology. We prove this for fake projective planes with non-abelian automorphism group (such as Keum's surface). Then by passing to equivariant categories we construct new examples of phantom categories with both Hochschild homology and Grothendieck group vanishing. 相似文献
3.
Norbert Knarr 《Journal of Geometry》1988,31(1-2):114-124
We show that a 4-dimensional connected abelian group can act in exactly five different ways as a collineation group of a compact 4-dimensional projective plane. Furthermore the complex projective plane is characterized as the only compact 4-dimensional projective plane which admits two different 4-dimensional abelian collineation groups.
Herrn Professor Dr. Eelmut Karzel zum 60. Geburtstag 相似文献
Herrn Professor Dr. Eelmut Karzel zum 60. Geburtstag 相似文献
4.
V. Braungardt 《Topology》2005,44(3):641-659
We prove that for every natural number k there are simply connected topological four-manifolds which have at least k distinct smooth structures supporting Einstein metrics, and also have infinitely many distinct smooth structures not supporting Einstein metrics. Moreover, all these smooth structures become diffeomorphic to each other after connected sum with only one copy of the complex projective plane. We prove that manifolds with these properties cover a large geographical area. 相似文献
5.
LetX be a complex, connected, projective surface. LetL be a very ample line bundle onX, i.e. there is an embedding :X P
c
with
. In this article we study projective classification for surfaces when the independent variable is large. 相似文献
6.
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
7.
Theo Grundhöfer 《Monatshefte für Mathematik》1988,105(4):261-277
Every compact disconnected projective plane can be written as an inverse limit of finite discrete incidence structures. Every finite projective plane is a continuous epimorphic image of some compact disconnected projective plane. There exist compact disconnected projective planes of Lenz type V which do not admit any continuous epimorphism onto a finite projective plane.Supported in part by a travel grant of the Deutsche Forschungsgemeinschaft. 相似文献
8.
Let X be a complex projective variety and consider the morphism
9.
M.A. Ivashkovskii 《Moscow University Mathematics Bulletin》2017,72(5):217-220
Immersions of graphs into the projective plane are studied. A classification of immersions up to a regular homotopy is obtained. A complete invariant of immersions up to a regular homotopy is constructed. The case of immersions of graphs into any compact surface differing from the projective plane was known previously. 相似文献
10.
Michael Lönne 《manuscripta mathematica》2000,103(4):455-464
The topological type of generalized Kummer surfaces is described in terms of sphere bundles over Riemann surfaces and the
complex projective plane. Explicit examples of sets of pairwise non-diffeomorphic K?hler surfaces of the same topological
type are given.
Received: 5 January 2000 相似文献
11.
M. Andreatta 《manuscripta mathematica》1995,87(1):359-367
LetX be a complex projective variety with log terminal singularities admitting an extremal contraction in terms of Minimal Model
Theory, i.e. a projective morphism φ:X→Z onto a normal varietyZ with connected fibers which is given by a (high multiple of a) divisor of the typeK
x+rL, wherer is a positive rational number andL is an ample Cartier divisor. We first prove that the dimension of anu fiberF of φ is bigger or equal to (r-1) and, if φ is birational, thatdimF≥r, with the equalities if and only ifF is the projective space andL the hyperplane bundle (this is a sort of “relative” version of a theorem of Kobayashi-Ochiai). Then we describe the structure
of the morphism φ itself in the case in which all fibers have minimal dimension with the respect tor. If φ is a birational divisorial contraction andX has terminal singularities we prove that φ is actually a “blow-up”. 相似文献
12.
Here we prove that every compact differential manifold has a smooth algebraic model defined over Q. In dimension 2 we find an algebraic model (may be singular) defined over Q and birational over Q to the projective plane. 相似文献
13.
Theo Grundhofer 《Geometriae Dedicata》1986,21(3):291-298
Compact connected projective planes have been investigated extensively in the last 30 years, mostly by studying their automorphism groups. It is our aim here to remove the connectedness assumption in some general results of Salzmann [31] and Hähl [14] on automorphism groups of compact projective planes. We show that the continuous collineations of every compact projective plane form a locally compact transformation group (Theorem 1), and that the continuous collineations fixing a quadrangle in a compact translation plane form a compact group (Corollary to Theorem 3). Furthermore we construct a metric for the topology of a quasifield belonging to a compact projective translation plane, using the modular function of its additive group (Theorem 2). 相似文献
14.
Let X be a complex connected projective nonsingular algebraic surface endowed with an ample line bundle L, which is spanned by its global sections. Pairs (X, L) as above, with sectional genus g(X, L)=1+(L·(K
X
L))/2=3 are classified by means of the main techniques of adjunction theory. 相似文献
15.
E. Ballico 《Annali dell'Universita di Ferrara》2002,48(1):21-23
LetX be a smooth complex compact surface without non-constant meromorphic functions. Here we prove the existence of rank holomorphic
vector bundles onX containing exactly one rank one saturated subsheaf.
Sunto SiaX una superficie complessa compatta non singolare senza funzioni meromorfe non costanti. In questo lavoro si domstra cheX possiede molti fibrati olomorfi di rango 2 contenenti un unico fibrato in rette.相似文献
16.
Grigory Mikhalkin 《Topology》2004,43(5):1035-1065
It is well-known that a Riemann surface can be decomposed into the so-called pairs-of-pants. Each pair-of-pants is diffeomorphic to a Riemann sphere minus 3 points. We show that a smooth complex projective hypersurface of arbitrary dimension admits a similar decomposition. The n-dimensional pair-of-pants is diffeomorphic to minus n+2 hyperplanes.Alternatively, these decompositions can be treated as certain fibrations on the hypersurfaces. We show that there exists a singular fibration on the hypersurface with an n-dimensional polyhedral complex as its base and a real n-torus as its fiber. The base accommodates the geometric genus of a hypersurface V. Its homotopy type is a wedge of hn,o(V) spheres Sn. 相似文献
17.
We introduce an intrinsic property for a projective variety as follows: there exists an embedding into some projective space such that the Gauss map is of rank zero, which we call (GMRZ) for short. It turns out that (GMRZ) imposes strong restrictions on rational curves on projective varieties: In fact, using (GMRZ), we show that, contrary to the characteristic zero case, the existence of free rational curves does not imply that of minimal free rational curves in positive characteristic case. We also focus attention on Segre varieties, Grassmann varieties, and hypersurfaces of low degree. In particular, we give a characterisation of Fermat cubic hypersurfaces in terms of (GMRZ), and show that a general hypersurface of low degree does not satisfy (GMRZ). 相似文献
18.
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
19.
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
20.
KEUM JongHae 《中国科学 数学(英文版)》2011,(8)
Given any (2,4)-elliptic surface with nine smooth rational curves,eight (2)-curves and one (3)-curve,forming a Dynkin diagram of type [2,2][2,2][2,2][2,2,3],we show that a fake projective plane can be constructed from it by taking a degree 3 cover and then a degree 7 cover.We also determine the types of singular fibres of such a (2,4)-elliptic surface. 相似文献