Explicit birational geometry of 3-folds and 4-folds of general type, III

DOI10.1112/S0010437X14007817zbMath1329.14030arXiv1302.0374MaRDI QIDQ3448429

Meng Chen, Jungkai Alfred Chen

Publication date: 23 October 2015

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.0374

zbMATH Keywords

linear systemspluricanonical mapsalgebraic fibrationsalgebraic 3-folds and 4-folds

Mathematics Subject Classification ID

Singularities in algebraic geometry (14B05) (4)-folds (14J35) (3)-folds (14J30) Rational and birational maps (14E05)

Related Items

On birational geometry of minimal threefolds with numerically trivial canonical divisors ⋮ Characterization of the 4-canonical birationality of algebraic threefolds. II ⋮ A reduction of canonical stability index of 4 and 5 dimensional projective varieties with large volume ⋮ Pluricanonical maps and the Fujita conjecture ⋮ On explicit birational geometry for minimal n$n$‐folds of canonical dimension n−1$n-1$ ⋮ Arithmetic and geometric deformations of threefolds ⋮ Classical algebraic geometry. Abstracts from the workshop held June 20--26, 2021 (hybrid meeting) ⋮ Boundedness of fibers for pluricanonical maps of varieties of general type ⋮ The canonical volume of minimal 3-folds of general type ⋮ On Severi type inequalities ⋮ Threefolds of Kodaira dimension one ⋮ On projective threefolds of general type with small positive geometric genus ⋮ On minimal 4-folds of general type with \(p_g \geq 2\) ⋮ The Noether inequality for algebraic \(3\)-folds. With an appendix by János Kollár.

Cites Work

• Some birationality criteria on 3-folds with \(p_g>1\)
• Explicit birational geometry of 3-folds of general type. II
• Flops connect minimal models
• Complex projective 3-fold with non-negative canonical Euler-Poincaré characteristic
• Finite generation of canonical ring by analytic method
• Pluricanonical systems on irregular 3-folds of general type
• A sharp lower bound for the canonical volume of 3-folds of general type
• A generalization of Kodaira-Ramanujam's vanishing theorem
• Tricanonical maps of numerical Godeaux surfaces
• On Kähler fiber spaces over curves
• Pluricanonical systems on algebraic varieties of general type
• Boundedness of pluricanonical maps of varieties of general type
• Canonical models of surfaces of general type
• Fibrations of low genus, I
• The canonical volume of 3-folds of general type with χ ⩽ 0
• Explicit birational geometry of threefolds of general type, I
• Existence of minimal models for varieties of log general type
• Flops
• Very ampleness of adjoint linear systems on smooth surfaces with boundary
• Canonical Stability of 3-Folds of General Type with p_g ≥ 3