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Abundance theorem for minimal projective varieties satisfying Miyaoka's equality
- Publication Year :
- 2024
-
Abstract
- In this paper, we solve the abundance conjecture for minimal projective klt varieties $X$ satisfying Miyaoka's equality $3c_2(X) = c_{1}(X)^{2}$. Specifically, we prove that the canonical divisor $K_{X}$ is semi-ample and the Kodaira dimension $\kappa(K_{X})$ is either $0$, $1$, or $2$. Moreover, according to the Kodaira dimension, we reveal the structure of the Iitaka fibration of $X$ up to quasi-\'etale covers. Additionally, we show similar results for projective klt varieties with nef anti-canonical divisor.<br />Comment: v2: 33pages; minor revison (We revised Introduction and added references) v1: 32 pages; comments are welcome
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2404.07568
- Document Type :
- Working Paper