Birational rigidity of quartic three-folds with a double point of rank 3
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A. V. Pukhlikov
Abstract
Let V be a general three-dimensional quartic in the complex projective space ℙ4 such that the only singularity of V is a double point of rank 3. We prove that V is a birationally rigid variety. Its group of birational self-maps is, up to the finite subgroup of biregular automorphisms, a free product of 25 cyclic groups of order 2. It follows that the complement to the set of birationally rigid factorial quartics with terminal singularities is of codimension at least 3 in the natural parameter space.
Acknowledgements
The author is grateful to the members of Divisions of Algebraic Geometry and Algebra at the Steklov Institute of Mathematics for the interest in his work, and also to the colleagues-algebraic geometers at the University of Liverpool for general support.
The author thanks the referee for their work on the paper.
Communicated by: R. Cavalieri
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© 2025 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Eigenforms of hyperelliptic curves with many automorphisms
- The optimal twisted paper cylinder
- Birational rigidity of quartic three-folds with a double point of rank 3
- Special divisors on real trigonal curves
- The Hoffman–Singleton manifold
- Classification of trees that quasi-inscribe rectangles in the hyperbolic plane
- Ramification points of homotopies: Enumeration and general theory
- On partially ample Ulrich bundles
- Rotational cmc surfaces in terms of Jacobi elliptic functions
- Locally classical stable planes
- Flocks in topological circle planes and their representation in generalised quadrangles
Artikel in diesem Heft
- Frontmatter
- Eigenforms of hyperelliptic curves with many automorphisms
- The optimal twisted paper cylinder
- Birational rigidity of quartic three-folds with a double point of rank 3
- Special divisors on real trigonal curves
- The Hoffman–Singleton manifold
- Classification of trees that quasi-inscribe rectangles in the hyperbolic plane
- Ramification points of homotopies: Enumeration and general theory
- On partially ample Ulrich bundles
- Rotational cmc surfaces in terms of Jacobi elliptic functions
- Locally classical stable planes
- Flocks in topological circle planes and their representation in generalised quadrangles
