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Algebraic cones of LCK manifolds with potential
- Source :
- Journal of Geometry and Physics Volume 198, April 2024, 105103
- Publication Year :
- 2022
-
Abstract
- A complex manifold $X$ is called "LCK manifolds with potential" if it can be realized as a complex submanifold of a Hopf manifold. Let $Y$ its $\Z$-covering, considered as a complex submanifold in $C^n \backslash 0$. We prove that $Y$ is algebraic. We call the manifolds obtained this way the algebraic cones, and show that the affine algebraic structure on $Y$ is independent from the choice of $X$. We give several intrinsic definitions of an algebraic cone, and prove that these definitions are equivalent.<br />Comment: 28 pages, LaTeX, v. 2.0, minor error corrected, intro rewritten
Details
- Database :
- arXiv
- Journal :
- Journal of Geometry and Physics Volume 198, April 2024, 105103
- Publication Type :
- Report
- Accession number :
- edsarx.2208.05833
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.geomphys.2024.105103