ν-PROJECTIVE SPACES, ν-LINE BUNDLES AND CHERN CLASSES

2011 ◽  
Vol 08 (02) ◽  
pp. 265-272 ◽  
Author(s):  
S. VARSAIE
Keyword(s):  
Special Kind ◽  
Projective Spaces ◽  
Line Bundles ◽  
Chern Classes

Following the formalism derived from one method of constructing common projective spaces along with using a special kind of odd module homomorphisms, denoted by ν, a novel supergeometric generalization of projective spaces is constructed. Existence of canonical line bundles over these spaces and their Chern classes are discussed.

VERONESE ARRANGEMENTS OF HYPERPLANES IN REAL PROJECTIVE SPACES

2012 ◽  
Vol 23 (05) ◽  
pp. 1250061 ◽  
Author(s):  
KOJI CHO ◽  
MASAAKI YOSHIDA
Keyword(s):  
General Position ◽  
Special Kind ◽  
Projective Spaces ◽  
Hyperplane Arrangements ◽  
The Real ◽  
Arrangements Of Hyperplanes

This paper studies chambers cut out by a special kind of hyperplane arrangements in general position, the Veronese arrangements, in the real projective spaces.

scholarly journals The index of harmonic maps from surfaces to complex projective spaces

2020 ◽  
Vol 31 (09) ◽  
pp. 2050069
Author(s):  
J. Oliver
Keyword(s):  
Projective Space ◽  
Lower Bounds ◽  
Complex Projective Space ◽  
Harmonic Maps ◽  
Projective Spaces ◽  
Line Bundles ◽  
Complex Projective Spaces ◽  
Holomorphic Sections ◽  
Higher Genus ◽  
Complex Projective

We estimate the dimensions of the spaces of holomorphic sections of certain line bundles to give improved lower bounds on the index of complex isotropic harmonic maps to complex projective space from the sphere and torus, and in some cases from higher genus surfaces.

scholarly journals P-Ample Bundles and Their Chern Classes

1971 ◽  
Vol 43 ◽  
pp. 91-116 ◽  
Author(s):  
David Gieseker
Keyword(s):  
Vector Bundle ◽  
Vector Bundles ◽  
Line Bundles ◽  
Chern Classes ◽  
Ground Field ◽  
Ample Vector Bundle

In [9], Hartshorne extended the concept of ampleness from line bundles to vector bundles. At that time, he conjectured that the appropriate Chern classes of an ample vector bundle were positive, and it was hoped that there would be some criterion for ampleness of vector bundles similar to Nakai’s criterion for line bundles. In the same paper, Hartshorne also introduced the notion of p-ample when the ground field had characteristic p, proved that a p-ample bundle was ample and asked if the converse were true.

CONIFOLD TRANSITIONS FOR COMPLETE INTERSECTION CALABI–YAU THREEFOLDS IN PRODUCTS OF PROJECTIVE SPACES

2013 ◽  
Vol 15 (04) ◽  
pp. 1350009
Author(s):  
JINXING XU
Keyword(s):  
Complete Intersection ◽  
Projective Spaces ◽  
Line Bundles ◽  
Complex Structures ◽  
Connected Sum ◽  
Connected Sums

We prove that a generic complete intersection Calabi–Yau threefold defined by sections of ample line bundles on a product of projective spaces admits a conifold transition to a connected sum of S3 × S3. In this manner, we obtain complex structures with trivial canonical bundles on some connected sums of S3 × S3. This construction is an analogue of that made by Friedman, Lu and Tian who used quintics in ℙ4.

A CRITERION FOR GETTING A BIG COMPONENT OF THE MODULI OF VECTOR BUNDLES BY CHANGING A POLARIZATION

2001 ◽  
Vol 12 (08) ◽  
pp. 927-942
Author(s):  
KIMIKO YAMADA
Keyword(s):  
Vector Bundles ◽  
Line Bundles ◽  
Closed Field ◽  
Projective Surface ◽  
Chern Classes ◽  
Algebraically Closed Field ◽  
Stable Vector Bundles ◽  
Normal Surfaces ◽  
Smooth Projective Surface ◽  
Moduli Of Vector Bundles

Let MH(c1, c2) be a coarse moduli scheme parameterizing all rank-two H-μ-stable vector bundles with Chern classes (c1, c2) on a smooth projective surface X over an algebraically closed field. For fixed two ample line bundles H and H′, it is known that if c2 is greater than some constant p(X, H, H′) depending on H and H′ then MH(c1, c2) and MH′(c1, c2) are birationally equivalent. In this paper we show that this constant p(X, H, H′) generally does depends on the choice of H and H′. More precisely, we give some example of surface (and c1) on which, for any number K, there exists an integer c2 with c2≥K such that sup H: ample dim MH(c1, c2) = + ∞. This result is available also for normal surfaces.

scholarly journals Relations in the cohomology ring of the moduli space of flat SO (2 n  + 1)-connections on a Riemann surface

2018 ◽  
Vol 376 (2131) ◽  
pp. 20170427
Author(s):  
Elisheva Adina Gamse ◽  
Jonathan Weitsman
Keyword(s):  
Riemann Surface ◽  
Moduli Space ◽  
Integrable Systems ◽  
Marked Point ◽  
Cohomology Ring ◽  
Line Bundles ◽  
Chern Classes ◽  
Theme Issue ◽  
Gauge Transformations ◽  
Finite Dimensional

We consider the moduli space of flat SO (2 n  + 1)-connections (up to gauge transformations) on a Riemann surface, with fixed holonomy around a marked point. There are natural line bundles over this moduli space; we construct geometric representatives for the Chern classes of these line bundles, and prove that the ring generated by these Chern classes vanishes below the dimension of the moduli space, generalizing a conjecture of Newstead. This article is part of the theme issue ‘Finite dimensional integrable systems: new trends and methods’.

scholarly journals Ample Vector Bundles on Curves

1971 ◽  
Vol 43 ◽  
pp. 73-89 ◽  
Author(s):  
Robin Hartshorne
Keyword(s):  
Vector Bundle ◽  
Vector Bundles ◽  
Line Bundles ◽  
Chern Classes ◽  
Intersection Numbers ◽  
Analytic Case ◽  
Roch Theorem

In our earlier paper [4] we developed the basic sheaftheoretic and cohomological properties of ample vector bundles. These generalize the corresponding well-known results for ample line bundles. The numerical properties of ample vector bundles are still poorly understood. For line bundles, Nakai’s criterion characterizes ampleness by the positivity of certain intersection numbers of the associated divisor with subvarieties of the ambient variety. For vector bundles, one would like to characterize ampleness by the numerical positivity of the Chern classes of the bundle (and perhaps of its restrictions to subvarieties and their quotients). Such a result, like the Riemann-Roch theorem, giving an equivalence between cohomological and numerical properties of a vector bundle, may be quite subtle. Some progress has been made by Gieseker [2], by Kleiman [8], and in the analytic case, by Griffiths [3].

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