论文标题
多stablelog calabi-yau品种和重力instantons
Polystable log Calabi-Yau varieties and Gravitational instantons
论文作者
论文摘要
几十年来，开放的calabi-yau歧管和log calabi-yau品种已被广泛研究。关于它们是“可分配”的对象，我们建议将它们视为良好的适当亚类，我们认为它们是某些多稳定的子类，在道德上与封闭（最小）轨道的半度相对应为GIT的经典类似物。 我们部分证实，新的多稳定性似乎等同于存在非紧密的完整ricci-flat Kahler指标，其体积较小，尤其是引力instantons的许多例子。另外，我们证明了一些紧凑或多stable还原类型的结果，部分是由紧凑型ricci-flat指标气泡的部分动机。
Open Calabi-Yau manifolds and log Calabi-Yau varieties have been broadly studied over decades. Regarding them as "semistable" objects, we propose to consider their good proper subclass, which we regard as certain poly-stable ones, morally corresponding to semistable with closed (minimal) orbits} as the classical analogue of GIT. We partially confirm that the new polystability seems equivalent to the existence of non-compact complete Ricci-flat Kahler metrics with small volume growths, notably many examples of gravitational instantons. Also, we prove some compactness or polystable reduction type results, partially motivated by bubbles of compact Ricci-flat metrics.
