论文标题
通用全体形态符号性品种的Kodaira维度
Kodaira dimension of universal holomorphic symplectic varieties
论文作者
论文摘要
我们证明，当n足够大时，晶状体偏振全态的圆锥形全体形态象征性品种的Kodaira尺寸稳定在模量时。然后，我们明确研究了Kodaira维度的过渡，从阴性到非负面，以实现已知的两极化符号品种的显式族。特别是，我们确定Beauville-Donagi和DeBarre-Voisin的确切过渡点，其中Borcherds phi_ {12}表格起着至关重要的作用。
We prove that the Kodaira dimension of the n-fold universal family of lattice-polarized holomorphic symplectic varieties with dominant and generically finite period map stabilizes to the moduli number when n is sufficiently large. Then we study the transition of Kodaira dimension explicitly, from negative to nonnegative, for known explicit families of polarized symplectic varieties. In particular, we determine the exact transition point in the cases of Beauville-Donagi and Debarre-Voisin, where the Borcherds Phi_{12} form plays a crucial role.
