论文标题
Segre四分之一的表面和MinitWistor空间
Segre quartic surfaces and minitwistor spaces
论文作者
论文摘要
标题中的Segre表面表示$ \ Mathbb {cp}^4 $中的四分之一表面，这是反典型地图下的弱del pezzo表面的图像。我们首先表明，具有属属的最小微型空间正好是Segre四分之一的表面。通过一种penrose对应关系，这些表面的投影双重品种的Zariski开放子集允许爱因斯坦 - 韦尔结构。我们详细研究了这些双重品种的结构。特别是，我们确定了这些品种的程度（即Segre表面的类别），以及边界分隔线的几个组成部分的结构，这些结构是投射双重品种中爱因斯坦 - 韦尔空间的补充。
Segre surfaces in the title mean quartic surfaces in $\mathbb{CP}^4$ which are the images of weak del Pezzo surfaces of degree four under the anti-canonical map. We first show that minimal minitwistor spaces with genus one are exactly Segre quartic surfaces. By a kind of Penrose correspondence, Zariski open subsets of the projective dual varieties of these surfaces admit Einstein-Weyl structure. We investigate structures of these dual varieties in detail. In particular, we determine the degrees of these varieties (namely the classes of the Segre surfaces), as well as structure of several components of the boundary divisors which are the complements of the Einstein-Weyl spaces in the projective dual varieties.
