论文标题
等级零DT不变性和OSV猜想的明确公式
Explicit formulae for rank zero DT invariants and the OSV conjecture
论文作者
论文摘要
修复满足Bogomolov-gieseker bayer-macrì-toda的bogomolov-gieseker猜想的3倍$ x $，例如3倍。通过两个不同的隔离性论点，我们证明了两种不同的公式等级为0唐纳森 - 托马斯不变式（对$ x $的扭转束带计数，在$ x $上支撑在富裕的除数上）。特别是，我们证明了Toda以$ x $的构图进行了稍作修改。当$ x $是PICARD排名第一时，我们还根据排名零和等级的DT不变式为等级的两个DT不变性提供了明确的公式。
Fix a Calabi-Yau 3-fold $X$ satisfying the Bogomolov-Gieseker conjecture of Bayer-Macrì-Toda, such as the quintic 3-fold. By two different wall-crossing arguments we prove two different explicit formulae relating rank 0 Donaldson-Thomas invariants (counting torsion sheaves on $X$ supported on ample divisors) in terms of rank 1 Donaldson-Thomas invariants (counting ideal sheaves of curves) and Pandharipande-Thomas invariants. In particular, we prove a slight modification of Toda's formulation of OSV conjecture for $X$. When $X$ is of Picard rank one, we also give an explicit formula for rank two DT invariants in terms of rank zero and rank one DT invariants.
