论文标题
划分两次的K3表面的曲线
Curves on K3 surfaces in divisibility two
论文作者
论文摘要
我们证明了毛利克，潘达里潘德（Pandharipande）和托马斯（Thomas）表达了gromov的gromov-在所有属的较弱的霍明型准形式方面，都在所有属的两种属中划分的k3表面两层的差异。然后，我们在所有属中建立了分别分配性的全态异常方程。我们的方法涉及光滑曲线模量空间的顶部重言式群，以及一个变性公式，用于减少具有不当曲线类别的虚拟基本类别。我们将与目标变量的双重分析关系用作证明初始条件的新工具。详细讨论了较高分裂性的全态异常方程与Oberdieck和Pandharipande的猜想多重覆盖公式之间的关系，并用几个示例进行了详细讨论。
We prove a conjecture of Maulik, Pandharipande, and Thomas expressing the Gromov--Witten invariants of K3 surfaces for divisibility two curve classes in all genus in terms of weakly holomorphic quasimodular forms of level two. Then, we establish the holomorphic anomaly equation in divisibility two in all genus. Our approach involves a refined boundary induction, relying on the top tautological group of the moduli space of smooth curves, together with a degeneration formula for reduced virtual fundamental class with imprimitive curve classes. We use the double ramification relations with target variety as a new tool to prove the initial condition. The relationship between the holomorphic anomaly equation for higher divisibility and the conjectural multiple cover formula of Oberdieck and Pandharipande is discussed in detail and illustrated with several examples.
