Affine cones over cubic surfaces are flexible in codimension one
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Alexander Perepechko
Abstract
Let Y be a smooth del Pezzo surface of degree 3 polarized by a very ample divisor that is not proportional to the anticanonical one. Then the affine cone over Y is flexible in codimension one. Equivalently, such a cone has an open subset with an infinitely transitive action of the special automorphism group on it.
Funding source: Russian Science Foundation
Award Identifier / Grant number: RSF-19-11-00172
Funding statement: The research was supported by the grant RSF-19-11-00172.
Acknowledgements
The author is grateful to M. G. Zaidenberg for everlasting motivation, numerous discussions and remarks, to I. Cheltsov and J. Park for useful discussions on the subject, and to I. Arzhantsev for valuable remarks and suggestions. The author thanks the referee for useful comments.
References
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Articles in the same Issue
- Frontmatter
- Lower bounds for regular genus and gem-complexity of PL 4-manifolds with boundary
- Free cyclic group actions on highly-connected 2n-manifolds
- The distinction problems for Sp4 and SO3,3
- Affine cones over cubic surfaces are flexible in codimension one
- Permutations of zero-sumsets in a finite vector space
- On the finiteness of solutions for polynomial-factorial Diophantine equations
- Galois action on Fuchsian surface groups and their solenoids
- On a Lévy process pinned at random time
- Borsuk–Ulam theorem for filtered spaces
- A non-commutative differential module approach to Alexander modules
- Generalized fractal dimensions of invariant measures of full-shift systems over compact and perfect spaces: generic behavior
- Quantum modularity of partial theta series with periodic coefficients
- Lyapunov-type inequalities for partial differential equations with 𝑝-Laplacian
- Zeros of GL2 𝐿-functions on the critical line
- Weighted boundedness of multilinear Calderón commutators
- Two characterizations of central BMO space via the commutators of Hardy operators
- Weyl 𝑛-algebras and the Swiss cheese operad
- Syzygies in equivariant cohomology in positive characteristic
- Epsilon factors of symplectic type characters in the wild case
