scholarly journals Mirror symmetry for concavex vector bundles on projective spaces

2003 ◽  
Vol 2003 (3) ◽  
pp. 159-197 ◽  
Author(s):  
Artur Elezi
Keyword(s):  
Mirror Symmetry ◽  
Vector Bundles ◽  
Projective Spaces ◽  
Witten Theory ◽  
Generic Section ◽  
Projective Manifolds ◽  
Local Mirror Symmetry ◽  
Zero Locus

LetX⊂Ybe smooth, projective manifolds. Assume thatι:X→ℙsis the zero locus of a generic section ofV+=⊕i∈I𝒪(ki), where all theki's are positive. Assume furthermore that𝒩X/Y=ι∗(V−), whereV−=⊕j∈J𝒪(−lj)and all thelj's are negative. We show that under appropriate restrictions, the generalized Gromov-Witten invariants ofXinherited fromYcan be calculated via a modified Gromov-Witten theory onℙs. This leads to local mirror symmetry on theA-side.

Projective manifolds of sectional genus three as zero loci of sections of ample vector bundles

2008 ◽  
Vol 144 (1) ◽  
pp. 109-118 ◽  
Author(s):  
ANTONIO LANTERI ◽  
HIDETOSHI MAEDA
Keyword(s):  
Vector Bundles ◽  
Projective Variety ◽  
Ample Line Bundle ◽  
Global Section ◽  
Sectional Genus ◽  
Ample Vector Bundle ◽  
Complex Projective Variety ◽  
Projective Manifolds ◽  
Complex Projective ◽  
Zero Locus

AbstractLet ϵ be an ample vector bundle of rank r ≥ 2 on a smooth complex projective variety X of dimension n such that there exists a global section of ϵ whose zero locus Z is a smooth subvariety of dimension n-r ≥ 2 of X. Let H be an ample line bundle on X such that the restriction HZ of H to Z is very ample. Triplets (X, ϵ, H) with g(Z, HZ) = 3 are classified, where g(Z, HZ) is the sectional genus of (Z, HZ).

AMPLE VECTOR BUNDLES WITH SECTIONS VANISHING ON PROJECTIVE SPACES OR QUADRICS

1995 ◽  
Vol 06 (04) ◽  
pp. 587-600 ◽  
Author(s):  
ANTONIO LANTERI ◽  
HIDETOSHI MAEDA
Keyword(s):  
Vector Bundle ◽  
Projective Space ◽  
Complex Manifold ◽  
Vector Bundles ◽  
Projective Spaces ◽  
Compact Complex Manifold ◽  
Ample Vector Bundle ◽  
Zero Locus

Let ɛ be an ample vector bundle of rank r≥2 on a compact complex manifold X of dimension n≥r+1 having a section whose zero locus is a submanifold Z of the expected dimension n–r. Pairs (X, ɛ) as above are classified under the assumption that Z is either a projective space or a quadric.

scholarly journals [N′-(4-Decyloxy-2-oxidobenzylidene)-3-hydroxy-2-naphthohydrazidato-κ3N,O,O′]dimethyltin(IV): crystal structure and Hirshfeld surface analysis

2017 ◽  
Vol 73 (3) ◽  
pp. 390-396
Author(s):  
Siti Nadiah Binti Mohd Rosely ◽  
Rusnah Syahila Duali Hussen ◽  
See Mun Lee ◽  
Nathan R. Halcovitch ◽  
Mukesh M. Jotani ◽  
...  
Keyword(s):  
Crystal Structure ◽  
Mirror Symmetry ◽  
Chelate Ring ◽  
Hirshfeld Surface ◽  
Methyl Groups ◽  
Coordination Geometry ◽  
Trigonal Bipyramidal ◽  
First Approximation ◽  
Benzene Rings ◽  
Local Mirror Symmetry

The title diorganotin compound, [Sn(CH3)2(C28H32N2O4)], features a distorted SnC2NO2coordination geometry almost intermediate between ideal trigonal–bipyramidal and square-pyramidal. The dianionic Schiff base ligand coordinates in a tridentate fashionviatwo alkoxide O and hydrazinyl N atoms; an intramolecular hydroxy-O—H...N(hydrazinyl) hydrogen bond is noted. The alkoxy chain has an all-transconformation, and to the first approximation, the molecule has local mirror symmetry relating the two Sn-bound methyl groups. Supramolecular layers sustained by imine-C—H...O(hydroxy), π–π [between decyloxy-substituted benzene rings with an inter-centroid separation of 3.7724 (13) Å], C—H...π(arene) and C—H...π(chelate ring) interactions are formed in the crystal; layers stack along thecaxis with no directional interactions between them. The presence of C—H...π(chelate ring) interactions in the crystal is clearly evident from an analysis of the calculated Hirshfeld surface.

scholarly journals Torus-equivariant vector bundles on projective spaces

1988 ◽  
Vol 111 ◽  
pp. 25-40 ◽  
Author(s):  
Tamafumi Kaneyama
Keyword(s):  
Vector Bundle ◽  
Toric Variety ◽  
Vector Bundles ◽  
Rational Point ◽  
Projective Spaces ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Algebraic Torus

For a free Z-module N of rank n, let T = TN be an n-dimensional algebraic torus over an algebraically closed field k defined by N. Let X = TN emb (Δ) be a smooth complete toric variety defined by a fan Δ (cf. [6]). Then T acts algebraically on X. A vector bundle E on X is said to be an equivariant vector bundle, if there exists an isomorphism ft: t*E → E for each k-rational point t in T, where t: X → X is the action of t. Equivariant vector bundles have T-linearizations (see Definition 1.2 and [2], [4]), hence we consider T-linearized vector bundles.

Ample Vector Bundles of Curve Genus One

1999 ◽  
Vol 42 (2) ◽  
pp. 209-213 ◽  
Author(s):  
Antonio Lanteri ◽  
Hidetoshi Maeda
Keyword(s):  
Vector Bundle ◽  
Vector Bundles ◽  
Projective Variety ◽  
Ample Vector Bundle ◽  
Smooth Complex ◽  
Complex Projective Variety ◽  
Curve Genus ◽  
Genus One ◽  
Complex Projective ◽  
Zero Locus

AbstractWe investigate the pairs (X, ε) consisting of a smooth complex projective variety X of dimension n and an ample vector bundle ε of rank n − 1 on X such that ε has a section whose zero locus is a smooth elliptic curve.

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