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Differential geometric global smoothings of simple normal crossing complex surfaces with trivial canonical bundle.
- Source :
- Complex Manifolds; Jan2023, Vol. 10 Issue 1, p1-38, 38p
- Publication Year :
- 2023
-
Abstract
- Let X X be a simple normal crossing (SNC) compact complex surface with trivial canonical bundle which includes triple intersections. We prove that if X X is d d -semistable, then there exists a family of smoothings in a differential geometric sense. This can be interpreted as a differential geometric analogue of the smoothability results due to Friedman, Kawamata-Namikawa, Felten-Filip-Ruddat, Chan-Leung-Ma, and others in algebraic geometry. The proof is based on an explicit construction of local smoothings around the singular locus of X X , and the first author's existence result of holomorphic volume forms on global smoothings of X X. In particular, these volume forms are given as solutions of a nonlinear elliptic partial differential equation. As an application, we provide several examples of d d -semistable SNC complex surfaces with trivial canonical bundle including double curves, which are smoothable to complex tori, primary Kodaira surfaces, and K 3 K3 surfaces. We also provide several examples of such complex surfaces including triple points, which are smoothable to K 3 K3 surfaces. [ABSTRACT FROM AUTHOR]
- Subjects :
- ALGEBRAIC geometry
Subjects
Details
- Language :
- English
- ISSN :
- 23007443
- Volume :
- 10
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Complex Manifolds
- Publication Type :
- Academic Journal
- Accession number :
- 162345274
- Full Text :
- https://doi.org/10.1515/coma-2022-0143