Correspondences of K3 surface via moduli of sheaves

K3曲面是代数曲面中最引人注目的一类曲面，在当代数学和物理学中有着重要的意义。在过去的40年里，人们对它们的认识有了很大的进展，但我们仍然发现了一些新的、意想不到的和重要的性质。，K3曲面的Picard格（由代数曲线生成）的元素在K3曲面与其自身的乘积上以及K3曲面与其自身的对应关系上提供显著的二维代数循环。当一个K3曲面上的相干层的模与一个给定的Mukai向量重合时，就会发生这种情况。我们要详细研究这一现象。

K3 surfaces is one of the most remarkable classes of algebraic surfaces which are very important in contemporary Mathematics and Physics. During last 40 years there was a big progress in their understanding, but we still discover some their new, unexpected and important properties. , elements of the Picard lattice (generated by algebraic curves) of a K3 surface deliver remarkable two-dimensional algebraic cycles on the product of the K3 surface with itself, and a correspondence of the K3 surface with itself. It happens when moduli of coherent sheaves over a K3 surface with a given Mukai vector coincide with this K3 surface. We want to study this phenomenon in details.