no code implementations • 3 Jul 2020 • Jingjun Han, Jihao Liu
For $\epsilon$-lc Fano type varieties $X$ of dimension $d$ and a given finite set $\Gamma$, we show that there exists a positive integer $m_0$ which only depends on $\epsilon, d$ and $\Gamma$, such that both $|-mK_X-\sum_i\lceil mb_i\rceil B_i|$ and $|-mK_X-\sum_i\lfloor mb_i\rfloor B_i|$ define birational maps for any $m\ge m_0$ provided that $B_i$ are pseudo-effective Weil divisors, $b_i\in\Gamma$, and $-(K_X+\sum_ib_iB_i)$ is big.
Algebraic Geometry
