论文标题
六倍的广义Kummer类型和K3表面
Sixfolds of generalized Kummer type and K3 surfaces
论文作者
论文摘要
我们证明，任何hyper-kähler六倍的$ k $的广义kummer类型都具有自然关联的歧管$ y_k $ of $ \ mathrm {k} 3^{[3]} $ - 类型。它作为$ k $的商的可鸡蛋分辨率，这是一组在其第二个共同体上行动的符合性的事物。当$ k $投影时，品种$ y_k $是在独特确定的投影量〜$ \ mathrm {k} 3 $ surface〜 $ s_k $上的稳定束带的模量空间。作为这种结构的应用，我们表明KGA-SATAKE对应是K3表面$ s_k $的代数，生产了无限的许多新家庭，$ \ mathrm {k} 3 $ PICARD等级的表面$ 16 $满足Kuga-Satake Hodge Hodge猜想。
We prove that any hyper-Kähler sixfold $K$ of generalized Kummer type has a naturally associated manifold $Y_K$ of $\mathrm{K}3^{[3]}$-type. It is obtained as crepant resolution of the quotient of $K$ by a group of symplectic involutions acting trivially on its second cohomology. When $K$ is projective, the variety $Y_K$ is birational to a moduli space of stable sheaves on a uniquely determined projective~$\mathrm{K}3$ surface~$S_K$. As application of this construction we show that the Kuga-Satake correspondence is algebraic for the K3 surfaces $S_K$, producing infinitely many new families of $\mathrm{K}3$ surfaces of general Picard rank $16$ satisfying the Kuga-Satake Hodge conjecture.
