Complex manifolds polarized by an ample and spanned line bundle of sectional genus three

1998 ◽  
Vol 71 (2) ◽  
pp. 159-168 ◽  
Author(s):  
Yoshiaki Fukuma ◽  
Hironobu Ishihara
Keyword(s):  
Line Bundle ◽  
Complex Manifolds ◽  
Sectional Genus

Classification of Algebraic Surfaces with Sectional Genus less than or Equal to Six. II: Ruled Surfaces with dim ϕKx⊗L(x) = l

1986 ◽  
Vol 38 (5) ◽  
pp. 1110-1121 ◽  
Author(s):  
Elvira Laura Livorni
Keyword(s):  
Line Bundle ◽  
Hyperplane Section ◽  
Ample Line Bundle ◽  
Rational Surface ◽  
Algebraic Surfaces ◽  
Sectional Genus ◽  
Rational Surfaces ◽  
Image Position ◽  
Smooth Hyperplane Section

Let L be a very ample line bundle on a smooth, connected, projective, ruled not rational surface X. We have considered the problem of classifying biholomorphically smooth, connected, projected, ruled, non rational surfaces X with smooth hyperplane section C such that the genus g = g(C) is less than or equal to six and dim where is the map associated to . L. Roth in [10] had given a birational classification of such surfaces. If g = 0 or 1 then X has been classified, see [8].If g = 2 ≠ hl,0(X) by [12, Lemma (2.2.2) ] it follows that X is a rational surface. Thus we can assume g ≦ 3.Since X is ruled, h2,0(X) = 0 andsee [4] and [12, p. 390].

scholarly journals Classification of algebraic non-ruled surfaces with sectional genus less than or equal to six

1985 ◽  
Vol 100 ◽  
pp. 1-9 ◽  
Author(s):  
Elvira Laura Livorni
Keyword(s):  
Line Bundle ◽  
Hyperplane Section ◽  
Ample Line Bundle ◽  
Ruled Surfaces ◽  
Sectional Genus ◽  
Rational Surfaces ◽  
Very Ample Line Bundle ◽  
Similar Classification

In this paper we have given a biholomorphic classification of smooth, connected, protective, non-ruled surfaces X with a smooth, connected, hyperplane section C relative to L, where L is a very ample line bundle on X, such that g = g(C) = g(L) is less than or equal to six. For a similar classification of rational surfaces with the same conditions see [Li].

scholarly journals The Local Structure of Generalized Contact Bundles

2019 ◽  
Vol 2020 (20) ◽  
pp. 6871-6925 ◽  
Author(s):  
Jonas Schnitzer ◽  
Luca Vitagliano
Keyword(s):  
Line Bundle ◽  
Symplectic Manifold ◽  
Complex Manifold ◽  
Local Structure ◽  
Complex Structure ◽  
Regular Point ◽  
Poisson Geometry ◽  
Splitting Theorem ◽  
Complex Manifolds ◽  
Generalized Complex

Abstract Generalized contact bundles are odd-dimensional analogues of generalized complex manifolds. They have been introduced recently and very little is known about them. In this paper we study their local structure. Specifically, we prove a local splitting theorem similar to those appearing in Poisson geometry. In particular, in a neighborhood of a regular point, a generalized contact bundle is either the product of a contact and a complex manifold or the product of a symplectic manifold and a manifold equipped with an integrable complex structure on the gauge algebroid of the trivial line bundle.

scholarly journals Explicit soft supersymmetry breaking in the heterotic M-theory B − L MSSM

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Anthony Ashmore ◽  
Sebastian Dumitru ◽  
Burt A. Ovrut
Keyword(s):  
Line Bundle ◽  
Supersymmetry Breaking ◽  
Moduli Space ◽  
Initial Conditions ◽  
Low Energy ◽  
Strongly Coupled ◽  
Hidden Sector ◽  
Effective Lagrangian ◽  
Soft Supersymmetry Breaking ◽  
M Theory

Abstract The strongly coupled heterotic M-theory vacuum for both the observable and hidden sectors of the B − L MSSM theory is reviewed, including a discussion of the “bundle” constraints that both the observable sector SU(4) vector bundle and the hidden sector bundle induced from a single line bundle must satisfy. Gaugino condensation is then introduced within this context, and the hidden sector bundles that exhibit gaugino condensation are presented. The condensation scale is computed, singling out one line bundle whose associated condensation scale is low enough to be compatible with the energy scales available at the LHC. The corresponding region of Kähler moduli space where all bundle constraints are satisfied is presented. The generic form of the moduli dependent F-terms due to a gaugino superpotential — which spontaneously break N = 1 supersymmetry in this sector — is presented and then given explicitly for the unique line bundle associated with the low condensation scale. The moduli-dependent coefficients for each of the gaugino and scalar field soft supersymmetry breaking terms are computed leading to a low-energy effective Lagrangian for the observable sector matter fields. We then show that at a large number of points in Kähler moduli space that satisfy all “bundle” constraints, these coefficients are initial conditions for the renormalization group equations which, at low energy, lead to completely realistic physics satisfying all phenomenological constraints. Finally, we show that a substantial number of these initial points also satisfy a final constraint arising from the quadratic Higgs-Higgs conjugate soft supersymmetry breaking term.

scholarly journals On the set of divisors with zero geometric defect

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Dinh Tuan Huynh ◽  
Duc-Viet Vu
Keyword(s):  
Line Bundle ◽  
Zero Divisor ◽  
Ample Line Bundle ◽  
Holomorphic Section ◽  
Projective Manifold ◽  
Holomorphic Curve ◽  
Very Ample Line Bundle ◽  
Complex Projective ◽  
Geometric Defect

AbstractLet {f:\mathbb{C}\to X} be a transcendental holomorphic curve into a complex projective manifold X. Let L be a very ample line bundle on {X.} Let s be a very generic holomorphic section of L and D the zero divisor given by {s.} We prove that the geometric defect of D (defect of truncation 1) with respect to f is zero. We also prove that f almost misses general enough analytic subsets on X of codimension 2.

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