论文标题
等级2分类问题I：比例不变几何。
The rank 2 classification problem I: scale invariant geometries
论文作者
论文摘要
在这三篇论文系列中的第一篇中，我们概述了一种方法来对4D $ \ MATHCAL {n} {n} {=} 2 $等级2的超级通用字段理论。允许的比例尺不变$ \ Mathcal $ \ Mathcal {n} = 2 $ coulomb coulomb分支（或等级）的尺寸（或等级）的空间更大的空间很大的空间$ \ MATHCAL {N} {=} 2 $ SUPERCONGORAL字段理论。在等级2，问题等同于找到所有可能的seiberg-witten曲线和满足特殊Kähler条件的1型曲线。这是可以进行处理的，因为常规属2 riemann表面可以均匀地描述为二进制隔离平面曲线，而塞伯格（Seiberg）编织的曲线是这种曲线的家族，在二维基础上有变化的曲线。还有一些解决方案，由退化属-2 riemann表面的家族组成，由两条椭圆曲线的花束给出，这些曲线由不同的曲线描述。在本文中，我们设置并进行了对通用情况的分析，即那些典型纤维是常规的属2 riemann表面的那些，没有扩展的自动形态，并找到了多项式系数的完整答案。
In this first of a series of three papers we outline an approach to classifying 4d $\mathcal{N}{=}2$ superconformal field theories at rank 2. The classification of allowed scale invariant $\mathcal{N}=2$ Coulomb branch geometries of dimension (or rank) greater than one is a famous open problem whose solution will greatly constrain the space of $\mathcal{N}{=}2$ superconformal field theories. At rank 2 the problem is equivalent to finding all possible genus 2 Seiberg-Witten curves and 1-forms satisfying a special Kähler condition. This is tractable because regular genus 2 Riemann surfaces can be uniformly described as binary-sextic plane curves, and the Seiberg-Witten curves are families of such curves varying meromorphically over the two-dimensional base. There are also solutions consisting of families of degenerate genus-2 Riemann surfaces given by a bouquet of two elliptic curves which are described by a different set of curves. In this paper we set up and carry out the analysis of the generic case, i.e., those whose typical fiber is a regular genus-2 Riemann surface with no extended automorphism, and find the complete answer for polynomial coefficients.
