论文标题
对数Donaldson-Thomas理论
Logarithmic Donaldson-Thomas theory
论文作者
论文摘要
让$ x $是平滑的三倍，带有简单的正常交叉分隔线$ d $。我们构建了$（x | d）的Donaldson-Thomas理论，相对于$ d $，$ x $列举了理想的滑轮。这些模量空间通过研究目标几何形状的扩展中的亚物种而被压缩，而模量空间带有虚拟基本类，导致具有预期特性的数值不变性。我们与标准理论并行制定守时，合理性和隔离猜想。我们的形式主义专长于当除数平滑时相对理想的束带的li-wu理论，并且与对数格罗莫夫（Gromov-witch）的最新作品相似，并具有扩展。
Let $X$ be a smooth threefold with a simple normal crossings divisor $D$. We construct the Donaldson-Thomas theory of the pair $(X|D)$ enumerating ideal sheaves on $X$ relative to $D$. These moduli spaces are compactified by studying subschemes in expansions of the target geometry, and the moduli space carries a virtual fundamental class leading to numerical invariants with expected properties. We formulate punctual evaluation, rationality and wall-crossing conjectures, in parallel with the standard theory. Our formalism specializes to the Li-Wu theory of relative ideal sheaves when the divisor is smooth, and is parallel to recent work on logarithmic Gromov-Witten theory with expansions.
