Book contents
- Frontmatter
- Dedicaton
- Contents
- Contributors
- Happy Birthday
- On Stable Cohomology of Central Extensions of Elementary Abelian Groups
- On Projective 3-Folds of General Type with pg = 2
- 15-Nodal Quartic Surfaces. Part I: Quintic del Pezzo Surfaces and Congruences of Lines in P3
- Mori Flips, Cluster Algebras and Diptych Varieties Without Unprojection
- The Mirror of the Cubic Surface
- Semi-Orthogonal Decomposition of a Derived Category of a 3-Fold With an Ordinary Double Point
- Duality and Normalization, Variations on a Theme of Serre and Reid
- Rationality of Q-Fano Threefolds of Large Fano Index
- An Exceptional Locus in the Perfect Compactification of Ag
- Variation of Stable Birational Types of Hypersurfaces
- Triangle Varieties and Surface Decomposition of Hyper-Käahler Manifolds
- References
An Exceptional Locus in the Perfect Compactification of Ag
Published online by Cambridge University Press: 25 October 2022
Book contents
- Frontmatter
- Dedicaton
- Contents
- Contributors
- Happy Birthday
- On Stable Cohomology of Central Extensions of Elementary Abelian Groups
- On Projective 3-Folds of General Type with pg = 2
- 15-Nodal Quartic Surfaces. Part I: Quintic del Pezzo Surfaces and Congruences of Lines in P3
- Mori Flips, Cluster Algebras and Diptych Varieties Without Unprojection
- The Mirror of the Cubic Surface
- Semi-Orthogonal Decomposition of a Derived Category of a 3-Fold With an Ordinary Double Point
- Duality and Normalization, Variations on a Theme of Serre and Reid
- Rationality of Q-Fano Threefolds of Large Fano Index
- An Exceptional Locus in the Perfect Compactification of Ag
- Variation of Stable Birational Types of Hypersurfaces
- Triangle Varieties and Surface Decomposition of Hyper-Käahler Manifolds
- References
Summary
We prove that Q-Fano threefolds of Fano index ≥ 8 are rational.
- Type
- Chapter
- Information
- Recent Developments in Algebraic GeometryTo Miles Reid for his 70th Birthday, pp. 275 - 295Publisher: Cambridge University PressPrint publication year: 2022
References
Ash, Avner, David Mumford, Michael Rapoport and Yung-Sheng Tai. Smooth compactifications of locally symmetric varieties. Cambridge Mathematical Library. Cambridge University Press, Cambridge, second edition, 2010. With the collaboration of Peter Scholze.CrossRefGoogle Scholar
Barnes, E. S. and M. J. Cohn. On the inner product of positive quadratic forms. J. London Math. Soc. (2), 12(1):32–36, 1975/76.CrossRefGoogle Scholar
Dolgachev and David Ortland. Point sets in projective spaces and theta functions. Astérisque, Igor, (165):210 pp. (1989), 1988.Google Scholar
Faltings and Ching-Li Chai. Degeneration of abelian varieties, volume 22 of Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Springer-Verlag, Gerd, Berlin, 1990. With an appendix by David Mumford.Google Scholar
Hassett, Brendan and Donghoon Hyeon. Log minimal model program for the moduli space of stable curves: the first flip. Ann. of Math. (2), 177(3):911–968, 2013.Google Scholar
W. H. T. Hudson. Kummer's quartic surface. Cambridge Mathematical Library. Cambridge University Press, R., Cambridge, 1990. With a foreword by W. Barth, Revised reprint of the 1905 original.Google Scholar
Keel, Sean. Basepoint freeness for nef and big line bundles in positive characteristic. Ann. of Math. (2), 149(1):253–286, 1999.Google Scholar
Keel, Sean and Shigefumi Mori. Quotients by groupoids. Ann. of Math. (2), 145(1):193–213, 1997.CrossRefGoogle Scholar
Kollar. Rational curves on algebraic varieties, volume 32 of Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics. Springer-Verlag, Janos, Berlin, 1996.Google Scholar
Shepherd-Barron, N. I.. Perfect forms and the moduli space of abelian varieties. Invent. Math., 163(1):25–45, 2006.CrossRefGoogle Scholar
S. Snurnikov. Quotients of canonical toric singularities. PhD thesis, V., University of Cambridge, 2002.Google Scholar
Tai, Yung-Sheng. On the Kodaira dimension of the moduli space of abelian varieties. Invent. Math., 68(3):425–439, 1982.Google Scholar