论文标题
带有实际系数的子对的有效的异性。
Effective birationality for sub-pairs with real coefficients
论文作者
论文摘要
对于$ε$ -lc fano类型品种$ x $ dimension $ d $和给定有限套件的$γ$，我们表明存在一个正整数$ m_0 $，仅取决于$ε，d $和$γ$ $|-mK_X-\sum_i\lfloor mb_i\rfloor B_i|$ define birational maps for any $m\ge m_0$ provided that $B_i$ are pseudo-effective Weil divisors, $b_i\inΓ$, and $-(K_X+\sum_ib_iB_i)$ is big.当$γ\ subset [0,1] $满足DCC但不是有限的时，我们构建了一个例子，以表明即使$ x $固定，有效的异常性也可能会失败，$ b_i $是固定的prime除数，而$（x，b）$ as $ε'$ -lc对于某些$ε'> 0 $。
For $ε$-lc Fano type varieties $X$ of dimension $d$ and a given finite set $Γ$, we show that there exists a positive integer $m_0$ which only depends on $ε,d$ and $Γ$, 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, $b_i\inΓ$, and $-(K_X+\sum_ib_iB_i)$ is big. When $Γ\subset[0,1]$ satisfies the DCC but is not finite, we construct an example to show that the effective birationality may fail even if $X$ is fixed, $B_i$ are fixed prime divisors, and $(X,B)$ is $ε'$-lc for some $ε'>0$.
