论文标题
伪有效的类别关于投影不可还原性全态形态歧管的类别
Pseudo-effective classes on projective irreducible holomorphic symplectic manifolds
论文作者
论文摘要
我们表明，Kovács在K3表面的曲线锥上的结果将推广到任何投影不可还原的全态象征歧管$ x $。特别是，我们表明，如果$ρ（x）\ geq 3 $，则伪有效的锥体$ \ edline {\ mathrm {eff}（x）（x）} $是圆形或等于$ \ operline {\ sum_ {e sum_ {e} {e} $ x $。证据通过双曲线几何形状以及（图像）hodge monodromy group $ \ mathrm {mon}^2 _ {\ mathrm {\ mathrm {hdg}}（x）$ in $ \ text {O}^+（n^1（x））$是有限的。如果$ x $属于已知的变形类之一，则携带优质的Divisor $ e $，而$ρ（x）\ geq 3 $，我们明确地构建了一个附加的积分有效除数，在数值上与$ e $相当，并具有相同的单型orbit，即$ e $。总而言之，我们提供了本文主要结果的一些后果，例如，我们在某些原始的符合性品种上获得了未释放的除数的存在。
We show that Kovács' result on the cone of curves of a K3 surface generalizes to any projective irreducible holomorphic symplectic manifold $X$. In particular, we show that if $ρ(X)\geq 3$, the pseudo-effective cone $\overline{\mathrm{Eff}(X)}$ is either circular or equal to $\overline{\sum_{E}\mathbf{R}^{\geq 0} [E]}$, where the sum runs over the prime exceptional divisors of $X$. The proof goes through hyperbolic geometry and the fact that (the image of) the Hodge monodromy group $\mathrm{Mon}^2_{\mathrm{Hdg}}(X)$ in $\text{O}^+(N^1(X))$ is of finite index. If $X$ belongs to one of the known deformation classes, carries a prime exceptional divisor $E$, and $ρ(X)\geq 3$, we explicitly construct an additional integral effective divisor, not numerically equivalent to $E$, with the same monodromy orbit as that of $E$. To conclude, we provide some consequences of the main result of the paper, for instance, we obtain the existence of uniruled divisors on certain primitive symplectic varieties.
