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Computing Riemann--Roch polynomials and classifying hyper-Kahler fourfolds.
- Source :
- Journal of the American Mathematical Society; 2024, Vol. 37 Issue 1, p151-185, 35p
- Publication Year :
- 2024
-
Abstract
- We prove that a hyper-Kähler fourfold satisfying a mild topological assumption is of K3^{[2]} deformation type. This proves in particular a conjecture of O'Grady stating that hyper-Kähler fourfolds of K3^{[2]} numerical type are of K3^{[2]} deformation type. Our topological assumption concerns the existence of two integral degree-2 cohomology classes satisfying certain numerical intersection conditions. There are two main ingredients in the proof. We first prove a topological version of the statement, by showing that our topological assumption forces the Betti numbers, the Fujiki constant, and the Huybrechts–Riemann–Roch polynomial of the hyper-Kähler fourfold to be the same as those of K3^{[2]} hyper-Kähler fourfolds. The key part of the article is then to prove the hyper-Kähler SYZ conjecture for hyper-Kähler fourfolds for divisor classes satisfying the numerical condition mentioned above. [ABSTRACT FROM AUTHOR]
- Subjects :
- POLYNOMIALS
BETTI numbers
LOGICAL prediction
Subjects
Details
- Language :
- English
- ISSN :
- 08940347
- Volume :
- 37
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Journal of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 174634777
- Full Text :
- https://doi.org/10.1090/jams/1016