scholarly journals Duality between the pseudoeffective and the movable cone on a projective manifold

2019 ◽  
Vol 32 (3) ◽  
pp. 675-689
Author(s):  
David Witt Nyström
Keyword(s):  
Projective Manifold

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.

scholarly journals KODAIRA DIMENSION OF SUBVARIETIES II

2006 ◽  
Vol 17 (05) ◽  
pp. 619-631 ◽  
Author(s):  
THOMAS PETERNELL
Keyword(s):  
Normal Bundle ◽  
General Type ◽  
Kodaira Dimension ◽  
Projective Manifold ◽  
Fundamental Groups ◽  
Weak Version ◽  
Joint Paper ◽  
Rationally Connected

This paper continues the study of non-general type subvarieties begun in a joint paper with Schneider and Sommese [14]. We prove uniruledness of a projective manifold containing a submanifold not of general type whose normal bundle has positivity properties and study moreover the rational quotient. We also relate the fundamental groups and a prove a cohomological criterion for a manifold to be rationally connected (weak version of a conjecture of Mumford).

scholarly journals The Walker Abel–Jacobi map descends

2021 ◽  
Author(s):  
Jeffrey D. Achter ◽  
Sebastian Casalaina-Martin ◽  
Charles Vial
Keyword(s):  
Abelian Variety ◽  
Projective Manifold ◽  
Field Of Definition ◽  
Definition Of ◽  
Complex Projective ◽  
Intermediate Jacobian ◽  
Cycle Classes ◽  
Coniveau Filtration

AbstractFor a complex projective manifold, Walker has defined a regular homomorphism lifting Griffiths’ Abel–Jacobi map on algebraically trivial cycle classes to a complex abelian variety, which admits a finite homomorphism to the Griffiths intermediate Jacobian. Recently Suzuki gave an alternate, Hodge-theoretic, construction of this Walker Abel–Jacobi map. We provide a third construction based on a general lifting property for surjective regular homomorphisms, and prove that the Walker Abel–Jacobi map descends canonically to any field of definition of the complex projective manifold. In addition, we determine the image of the l-adic Bloch map restricted to algebraically trivial cycle classes in terms of the coniveau filtration.

scholarly journals Complex algebraic compactifications of the moduli space of Hermitian Yang–Mills connections on a projective manifold

2021 ◽  
Vol 25 (4) ◽  
pp. 1719-1818
Author(s):  
Daniel Greb ◽  
Benjamin Sibley ◽  
Matei Toma ◽  
Richard Wentworth
Keyword(s):  
Moduli Space ◽  
Projective Manifold ◽  
Yang Mills

scholarly journals Holomorphic Functions of Slow Growth on Nested Covering Spaces of Compact Manifolds

2000 ◽  
Vol 52 (5) ◽  
pp. 982-998 ◽  
Author(s):  
Finnur Lárusson
Keyword(s):  
Riemann Surfaces ◽  
Bergman Spaces ◽  
Holomorphic Functions ◽  
Weighted Bergman Spaces ◽  
Projective Manifold ◽  
Important Special Case ◽  
Covering Group ◽  
Bounded Holomorphic Function ◽  
Domains Of Holomorphy ◽  
Bounded Holomorphic

AbstractLet Y be an infinite covering space of a projective manifold M in N of dimension n ≥ 2. Let C be the intersection with M of at most n − 1 generic hypersurfaces of degree d in N. The preimage X of C in Y is a connected submanifold. Let φ be the smoothed distance from a fixed point in Y in a metric pulled up from M. Let φ(X) be the Hilbert space of holomorphic functions f on X such that f2e−φ is integrable on X, and define φ(Y) similarly. Our main result is that (under more general hypotheses than described here) the restriction φ(Y) → φ(X) is an isomorphism for d large enough.This yields new examples of Riemann surfaces and domains of holomorphy in n with corona. We consider the important special case when Y is the unit ball in n, and show that for d large enough, every bounded holomorphic function on X extends to a unique function in the intersection of all the nontrivial weighted Bergman spaces on . Finally, assuming that the covering group is arithmetic, we establish three dichotomies concerning the extension of bounded holomorphic and harmonic functions from X to .

scholarly journals ADJUNCTION FOR VARIETIES WITH A ℂ* ACTION

2020 ◽  
Author(s):  
ELEONORA A. ROMANO ◽  
JAROSŁAW A. WIŚNIEWSKI
Keyword(s):  
Fixed Point ◽  
Line Bundle ◽  
Normal Bundle ◽  
Ample Line Bundle ◽  
Projective Manifold ◽  
Fano Manifolds ◽  
Adjunction Theory ◽  
Rank 2 ◽  
General Orbit ◽  
Complex Projective

Abstract Let X be a complex projective manifold, L an ample line bundle on X, and assume that we have a ℂ* action on (X;L). We classify such triples (X; L;ℂ*) for which the closure of a general orbit of the ℂ* action is of degree ≤ 3 with respect to L and, in addition, the source and the sink of the action are isolated fixed points, and the ℂ* action on the normal bundle of every fixed point component has weights ±1. We treat this situation by relating it to the classical adjunction theory. As an application, we prove that contact Fano manifolds of dimension 11 and 13 are homogeneous if their group of automorphisms is reductive of rank ≥ 2.

scholarly journals PROJECTIVITY CRITERION OF MOISHEZON SPACES AND DENSITY OF PROJECTIVE SYMPLECTIC VARIETIES

2002 ◽  
Vol 13 (02) ◽  
pp. 125-135 ◽  
Author(s):  
YOSHINORI NAMIKAWA
Keyword(s):  
Kähler Manifold ◽  
Projective Manifold ◽  
Singular Case ◽  
Isolated Singularities ◽  
Rational Singularities ◽  
Kahler Manifold ◽  
Moishezon Space ◽  
Symplectic Varieties

A Moishezon manifold is a projective manifold if and only if it is a Kähler manifold [13]. However, a singular Moishezon space is not generally projective even if it is a Kähler space [14]. Vuono [19] has given a projectivity criterion for Moishezon spaces with isolated singularities. In this paper we shall prove that a Moishezon space with 1-rational singularities is projective when it is a Kähler space (Theorem 1.6). We shall use Theorem 1.6 to show the density of projective symplectic varieties in the Kuranishi family of a (singular) symplectic variety (Theorem 2.4), which is a generalization of the result by Fujiki [4, Theorem 4.8] to the singular case. In the Appendix we give a supplement and a correction to the previous paper [15] where singular symplectic varieties are dealt with.

scholarly journals PROJECTIVE AND CONFORMAL SCHWARZIAN DERIVATIVES AND COHOMOLOGY OF LIE ALGEBRAS VECTOR FIELDS RELATED TO DIFFERENTIAL OPERATORS

2006 ◽  
Vol 03 (04) ◽  
pp. 667-696 ◽  
Author(s):  
SOFIANE BOUARROUDJ
Keyword(s):  
Lie Algebras ◽  
Cohomology Group ◽  
Vector Fields ◽  
Differential Operators ◽  
Projective Manifold ◽  
Conformal Class ◽  
Tensor Fields ◽  
Relative Cohomology ◽  
Schwarzian Derivatives ◽  
Cohomology Of Lie Algebras

Let M be either a projective manifold (M, Π) or a pseudo-Riemannian manifold (M, g). We extend, intrinsically, the projective/conformal Schwarzian derivatives we have introduced recently, to the space of differential operators acting on symmetric contravariant tensor fields of any degree on M. As operators, we show that the projective/conformal Schwarzian derivatives depend only on the projective connection Π and the conformal class of the metric [g], respectively. Furthermore, we compute the first cohomology group of Vect(M) with coefficients in the space of symmetric contravariant tensor fields valued in the space of δ-densities, and we compute the corresponding sl(n + 1, ℝ)-relative cohomology group.

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