scholarly journals Projective bundles and blowing ups

2021 ◽  
Vol 359 (9) ◽  
pp. 1129-1133
Author(s):  
Duo Li
Keyword(s):  
Projective Bundles

scholarly journals Numerical Criteria for Very Ampleness of Divisors on Projective Bundles Over an Elliptic Curve

1996 ◽  
Vol 48 (6) ◽  
pp. 1121-1137 ◽  
Author(s):  
Alberto Alzati ◽  
Marina Bertolini ◽  
Gian Mario Besana
Keyword(s):  
Elliptic Curve ◽  
Numerical Characterization ◽  
Projective Bundles ◽  
Very Ampleness

AbstractLet D be a divisor on a projectivized bundle over an elliptic curve. Numerical conditions for the very ampleness of D are proved. In some cases a complete numerical characterization is found.

scholarly journals Delta invariants of projective bundles and projective cones of Fano type

2021 ◽  
Author(s):  
Kewei Zhang ◽  
Chuyu Zhou
Keyword(s):  
Projective Bundles

AbstractIn this paper, we will give a precise formula to compute delta invariants of projective bundles and projective cones of Fano type.

scholarly journals Projective bundles over small covers and the bundle triviality problem

2016 ◽  
Vol 28 (4) ◽  
Author(s):  
Shintarô Kuroki ◽  
Zhi Lü
Keyword(s):  
Convex Polytopes ◽  
Necessary And Sufficient Condition ◽  
Real Projective Space ◽  
Real Vector ◽  
Small Cover ◽  
Projective Bundles ◽  
Tautological Line Bundle ◽  
Necessary And Sufficient ◽  
Open Question ◽  
Simple Convex

AbstractThe present paper investigates the projective bundles over small covers. We first give a necessary and sufficient condition for the projectivization of a real vector bundle over a small cover to be a small cover. Then associated with moment-angle manifolds, we further study the structure of such a projectivization as a small cover by introducing a new characteristic function on simple convex polytopes. As an application, we characterize the real projective bundles over 2-dimensional small covers by interpreting the fiber sum operation to some combinatorial operation. We next determine when the projectivization of Whitney sum of the tautological line bundle and the tangent bundle over real projective space is diffeomorphic to the product of two real projective spaces. This answers an open question regarding the topology of the fiber of the Monster-Semple tower.

scholarly journals The Double Complex of a Blow-up

2019 ◽  
Author(s):  
Jonas Stelzig
Keyword(s):  
Blow Up ◽  
Differential Forms ◽  
Complex Manifolds ◽  
Double Complex ◽  
Smooth Complex ◽  
Projective Bundles ◽  
De Rham ◽  
Suitable Notion ◽  
Complex Valued ◽  
Compact Complex Manifolds

AbstractWe compute the double complex of smooth complex-valued differential forms on projective bundles over and blow-ups of compact complex manifolds up to a suitable notion of quasi-isomorphism. This simultaneously yields formulas for “all” cohomologies naturally associated with this complex (in particular, de Rham, Dolbeault, Bott–Chern, and Aeppli).

Projective bundles and their Chow rings

2016 ◽  
pp. 323-361
Author(s):  
David Eisenbud ◽  
Joe Harris
Keyword(s):  
Chow Rings ◽  
Projective Bundles

scholarly journals Projective bundles over toric surfaces

2016 ◽  
Vol 27 (04) ◽  
pp. 1650032 ◽  
Author(s):  
Suyoung Choi ◽  
Seonjeong Park
Keyword(s):  
Toric Variety ◽  
Cohomology Ring ◽  
Line Bundles ◽  
Projective Bundle ◽  
Cohomology Rings ◽  
Toric Surfaces ◽  
Projective Bundles ◽  
Higher Dimensional ◽  
Quasitoric Manifolds

Let [Formula: see text] be the Whitney sum of complex line bundles over a topological space [Formula: see text]. Then, the projectivization [Formula: see text] of [Formula: see text] is called a projective bundle over [Formula: see text]. If [Formula: see text] is a nonsingular complete toric variety, then so is [Formula: see text]. In this paper, we show that the cohomology ring of a nonsingular projective toric variety [Formula: see text] determines whether it admits a projective bundle structure over a nonsingular complete toric surface. In addition, we show that two [Formula: see text]-dimensional projective bundles over [Formula: see text]-dimensional quasitoric manifolds are diffeomorphic if their cohomology rings are isomorphic as graded rings. Furthermore, we study the smooth classification of higher dimensional projective bundles over [Formula: see text]-dimensional quasitoric manifolds.

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