On Shokurov's rational connectedness conjecture
From MaRDI portal
Publication:2370125
DOI10.1215/S0012-7094-07-13813-4zbMath1128.14028arXivmath/0504330OpenAlexW2070242545WikidataQ123013040 ScholiaQ123013040MaRDI QIDQ2370125
James McKernan, Christopher Derek Hacon
Publication date: 22 June 2007
Published in: Duke Mathematical Journal (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0504330
Singularities of surfaces or higher-dimensional varieties (14J17) Rational and birational maps (14E05) Fano varieties (14J45) Minimal model program (Mori theory, extremal rays) (14E30)
Related Items
Strong rational connectedness of surfaces, On weak Fano varieties with log canonical singularities, On relative rational chain connectedness of threefolds with anti-big canonical divisors in positive characteristics, Potentially non-klt locus and its applications, Geometric interpretation of toroidal compactifications of moduli of points in the line and cubic surfaces, Codimension \(1\) foliations with numerically trivial canonical class on singular spaces, The global moduli theory of symplectic varieties, A global Torelli theorem for singular symplectic varieties, On birational involutions of $ \mathbb P^3$, Rational curves on genus-one fibrations, Rational curves on complex manifolds, Simple connectedness of Fano log pairs with semi-log canonical singularities, Moduli of surfaces in, Geometric consistency of Manin's conjecture, On the connectedness principle and dual complexes for generalized pairs, Rationality does not specialize among terminal fourfolds, Algebraic varieties with automorphism groups of maximal rank, Deformations of \(\mathbb {A}^1\)-cylindrical varieties, Uniruledness of some low-dimensional ball quotients, Connected algebraic subgroups of groups of birational transformations not contained in a maximal one, On asymptotic base loci of relative anti-canonical divisors of algebraic fiber spaces, Coregularity of Fano varieties, A note on polarized varieties with high nef value, Geometric properties of projective manifolds of small degree, Rationality does not specialise among terminal varieties, Open problems on structure of positively curved projective varieties, On the log abundance for compact Kähler threefolds, The nonvanishing problem for varieties with nef anticanonical bundle, Fano Shimura varieties with mostly branched cusps, Jacobian discrepancies and rational singularities, Pull-back morphisms for reflexive differential forms, Singularities and syzygies of secant varieties of nonsingular projective curves, Invariant hypersurfaces of endomorphisms of projective varieties, Birational boundedness of rationally connected Calabi-Yau 3-folds, On uniruled degenerations of algebraic varieties with trivial canonical divisor, On codimension 1 del Pezzo foliations on varieties with mild singularities, Ampleness of canonical divisors of hyperbolic normal projective varieties, Structure of Fano fibrations of varieties admitting an int-amplified endomorphism, Bounding non-rationality of divisors on 3-fold Fano fibrations, Birational rigidity of complete intersections, Characterization of the 4-canonical birationality of algebraic threefolds, A geometric characterization of toric varieties, Behavior of canonical divisors under purely inseparable base changes, The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension, Positivity criteria for log canonical divisors and hyperbolicity, Special test configuration and \(K\)-stability of Fano varieties, Differential forms on log canonical spaces, Singular rationally connected surfaces with nonzero pluri-forms, Quotients of Calabi–Yau Varieties, Anti-pluricanonical systems on Fano varieties, Rational points on log Fano threefolds over a finite field, Balanced line bundles on Fano varieties, Boundedness of pluricanonical maps of varieties of general type, Projectively flat klt varieties, Hypersurfaces that are not stably rational, Nonabelian Hodge theory for klt spaces and descent theorems for vector bundles, Nef anti-canonical divisors and rationally connected fibrations, The dual complex of log Calabi-Yau pairs on Mori fibre spaces, Degenerations of rationally connected varieties, On exceptional sets in Manin's conjecture, Manin's \(b\)-constant in families, Regularity of structure sheaves of varieties with isolated singularities, On anticanonical volumes of weak Q-Fano terminal threefolds of Picard rank two, Rational curves and strictly nef divisors on Calabi-Yau threefolds, A characterization of complex quasi-projective manifolds uniformized by unit balls, Hyperbolicity for log canonical pairs and the cone theorem, A gap theorem for minimal log discrepancies of noncanonical singularities in dimension three, Unnamed Item, On rational connectedness of globally \(F\)-regular threefolds, Hyperbolicity and specialness of symmetric powers, Numerical characterization of some toric fiber bundles
Cites Work
- Unnamed Item
- Unnamed Item
- On twistor spaces of the class \({\mathcal C}\)
- A numerical criterion for uniruledness
- Projective manifolds with ample tangent bundles
- On Fujita's freeness conjecture for 3-folds and 4-folds
- Boundedness of pluricanonical maps of varieties of general type
- On the Valuations Centered in a Local Domain
- Rational connectedness of log Q-Fano varieties
- Rational curves on quasi-projective surfaces
- Diagram Method for 3-Folds and its Application to Kahler Cone and Picard Number of Calabi-Yau 3-Folds, I. with Appendix by Vyacheslav V. Shokurov: "Anticanonical boundedness for curves"
- Families of rationally connected varieties