On birational geometry of minimal threefolds with numerically trivial canonical divisors

Abstract

For a minimal $3$-fold $X$ with $K_X\equiv 0$ and a nef and big Weil divisor $L$ on $X$, we investigate the birational geometry inspired by $L$. We prove that $|mL|$ and $|K_X+mL|$ give birational maps for all $m\ge 17$. The result remains true under weaker assumption that $L$ is big and has no stable base components.

25pages. Final version. To appear in Math. Ann. arXiv admin note: text overlap with arXiv:0901.0413 by other authors. text overlap with arXiv:1408.6349

References in corpus (1)

• Explicit birational geometry of 3-folds and 4-folds of general type, III

Cited by in corpus (4)

• Miyaoka type inequality for terminal threefolds with nef anti-canonical divisors
• On the anti-canonical geometry of weak $\mathbb{Q}$-Fano threefolds, III
• Second Chern class of Fano manifolds and anti-canonical geometry
• On irregular threefolds and fourfolds with numerically trivial canonical bundle