Effective results in the three-dimensional minimal model program

DOI10.4171/icm2022/30arXiv2108.13052OpenAlexW3197250023MaRDI QIDQ6119704

Yuri G. Prokhorov

Publication date: 24 March 2024

Published in: International Congress of Mathematicians (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2108.13052

zbMATH Keywords

flipextremal rayminimal modelMori contractionterminal (canonical) singularity

Mathematics Subject Classification ID

Singularities in algebraic geometry (14B05) (3)-folds (14J30) Rational and birational maps (14E05) Minimal model program (Mori theory, extremal rays) (14E30) Rationality questions in algebraic geometry (14E08)

Cites Work

• Threefold extremal contractions of type (IA)
• \(\mathbb Q\)-Fano threefolds of large Fano index. I.
• Geography of log models: theory and applications
• A note on degenerations of del Pezzo surfaces
• Three-fold divisorial contractions to singularities of higher indices
• On \(\mathbb Q\)-conic bundles
• An optimal boundedness on weak \(\mathbb Q\)-Fano 3-folds
• On \(\mathbb Q\)-conic bundles. III.
• Threefolds and deformations of surface singularities
• Crepant blowing-up of 3-dimensional canonical singularities and its application to degenerations of surfaces
• Real algebraic threefolds. III. Conic bundles
• Elementary contractions of Gorenstein threefolds
• Blowing ups of 3-dimensional terminal singularities. II
• Blowing ups of 3-dimensional terminal singularities
• Log-canonical degenerations of del Pezzo surfaces in \(\mathbb{Q}\)-Gorenstein families
• Multiple fibers of del Pezzo fibrations
• Del Pezzo and \(K3\) surfaces
• On \(\mathbb Q\)-conic bundles. II
• Divisorial contractions to 3-dimensional terminal singularities with discrepancy one
• Three dimensional divisorial extremal neighborhoods
• On compact analytic surfaces. II
• Singularities of linear systems and boundedness of Fano varieties
• Supplement to classification of threefold divisorial contractions
• Flipping surfaces
• Fano 3-folds in codimension 4, Tom and Jerry. Part I
• Smoothable del Pezzo surfaces with quotient singularities
• Existence of minimal models for varieties of log general type
• Existence of minimal models for varieties of log general type II
• On 3-dimensional terminal singularities
• THE NONVANISHING THEOREM
• Flip Theorem and the Existence of Minimal Models for 3-Folds
• Classification of Three-Dimensional Flips
• 3-FOLD LOG FLIPS
• A rationality criterion for conic bundles
• Terminal 3-fold Divisorial Contractions of a Surface to a Curve I
• The rationality problem for conic bundles
• Families of D-minimal models and applications to 3-fold divisorial contractions
• General elephants of three-fold divisorial contractions
• The Sarkisov program
• Threefold extremal curve germs with one non-Gorenstein point
• General elephants for threefold extremal contractions with one-dimensional fibres: exceptional case
• BIRATIONAL GEOMETRY OF ALGEBRAIC VARIETIES
• Equivariant minimal model program
• The index of a threefold canonical singularity
• THREE-FOLD DIVISORIAL EXTREMAL NEIGHBORHOODS OVER cE₇ AND c₆ COMPOUND DUVAL SINGULARITIES
• Deforming elephants of Q‐Fano 3‐folds
• The degree of $ \mathbb Q$-Fano threefolds
• 3-Fold Extremal Contractions of Types (IC) and (IIB)
• Threefold extremal contractions of type (IIA). I
• Normal degenerations of the complex projective plane.
• Threefolds whose canonical bundles are not numerically effective
• Lectures on complements on log surfaces
• Divisorial contractions in dimension three which contract divisors to smooth points
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item