论文标题
曲线计数和s偶尔
Curve counting and S-duality
论文作者
论文摘要
我们在一个投影三倍的$ x $上工作，该$ x $满足了拜耳 - 麦克拉 - 托达（Bogomolov-Gieseker）的猜想，例如$ \ mathbb p^3 $或五重的三倍。 我们证明了$ x $上的二维扭转束带的某些模量空间是弯曲曲线的希尔伯特方案的平滑束，$ x $中的曲线和点。 当$ x $是calabi-yau时，这给出了一个简单的墙壁交叉公式表达曲线的数量（以及最终是gromov-witten的不变式），就D4-D2-D0 Branes的计数而言。这些后一种不变性被预测具有模块化特性，我们从S-偶尔和Noether-Lefschetz理论的角度讨论了模块化特性。
We work on a projective threefold $X$ which satisfies the Bogomolov-Gieseker conjecture of Bayer-Macrì-Toda, such as $\mathbb P^3$ or the quintic threefold. We prove certain moduli spaces of 2-dimensional torsion sheaves on $X$ are smooth bundles over Hilbert schemes of ideal sheaves of curves and points in $X$. When $X$ is Calabi-Yau this gives a simple wall crossing formula expressing curve counts (and so ultimately Gromov-Witten invariants) in terms of counts of D4-D2-D0 branes. These latter invariants are predicted to have modular properties which we discuss from the point of view of S-duality and Noether-Lefschetz theory.
