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
15-Nodal Quartic Surfaces. Part I: Quintic del Pezzo Surfaces and Congruences of Lines in P3
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 explain a classical construction of a del Pezzo surface of degree d = 4 or 5 as a smooth order 2 congruence of lines in P3 whose focal surface is a quartic surface X20-d with 20-d ordinary double points. We also show that X15 can be realized as a hyperplane section of the Castelnuovo– Richmond–Igusa quartic hypersurface in P4. This leads to the proof of rationality of the moduli space of 15-nodal quartic surfaces. We discuss some other birational models of X15: quartic symmetroids, 5-nodal quartic surfaces, 10-nodal sextic surfaces in P4 and nonsingular surfaces of degree 10 in P6. Finally we study some birational involutions of a 15- nodal quartic surface which, as it is shown in Part II of the paper jointly with I. Shimada [DS20], belong to a finite set of generators of the group of birational automorphisms of a general 15 nodal quartic surface.
- Type
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- Information
- Recent Developments in Algebraic GeometryTo Miles Reid for his 70th Birthday, pp. 66 - 115Publisher: Cambridge University PressPrint publication year: 2022
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