论文标题
异国情调的表面
Exotic surfaces
论文作者
论文摘要
我们通过理性的排列构建了第一个异国情调的$ \ Mathbb C \ Mathbb P^2 \＃4 \ ediLline {\ Mathbb C \ Mathbb P^2} $。同样，我们构建了第一个异国情调的$ 3 \ Mathbb C \ Mathbb P^2 \＃b^ - \ overline {\ Mathbb C \ Mathbb p^2} $ for $ b^ - = 9,8,7 $。它们都是最小和符合性的，因为它们是由带有wahl奇点的投影表面$ w $以及$ k_w $ big and nef生产的。在更普遍的情况下，我们详细介绍了找到异国$（2χ（\ Mathcal {o} _W）-1）-1）\ Mathbb C \ Mathbb p^2 \＃（10χ（\ Mathcal {o}} _W）-K^2_w-w） kollár--------------alexeev表面$ w $，获得明确的几何障碍物。
We construct the first exotic $\mathbb C \mathbb P^2 \# 4 \overline{\mathbb C \mathbb P^2}$ by means of rational blowdowns. Similarly, we construct the first exotic $3\mathbb C \mathbb P^2 \# b^- \overline{\mathbb C \mathbb P^2}$ for $b^-=9,8,7$ . All of them are minimal and symplectic, as they are produced from projective surfaces $W$ with Wahl singularities, and $K_W$ big and nef. In more generality, we elaborate on the problem of finding exotic $(2χ(\mathcal{O}_W)-1) \mathbb C \mathbb P^2 \# (10χ(\mathcal{O}_W)-K^2_W-1) \overline{\mathbb C \mathbb P^2}$ from these Kollár--Shepherd-Barron--Alexeev surfaces $W$, obtaining explicit geometric obstructions.
