环面或诺维科夫型基上的稳定性理论与典范修正
Stability theory over toroidal or Novikov type base and Canonical modifications
AI总结：
本文将代数几何中的稳定性理论推广到环面簇及其解析类似物，建立朗顿型Θ分层的（半）稳定约化定理，还探讨诺维科夫型环的应用，为K-稳定性与凯勒几何问题提供新框架。
摘要：
我们将代数几何中普遍存在的单参数族及其在稳定性理论（[GIT, HL, AHLH]）中的应用推广到环面簇及其解析类似物上的族。该语言使我们能将文献中“无理”方向的退化统一重述为典范对象。据此，我们将[AHLH]中朗顿型的Θ分层的（半）稳定约化型定理推广到更高秩的情形。我们还建立了该结果的复解析类似物。作为环面谱的无穷小类似物，我们使用诺维科夫型环，因其能提供更强的典范性，但逻辑上不使用此类环的读者也可避开。我们的其他论文讨论该框架及主要定理在K-稳定性与凯勒几何相关问题中的应用。
英文摘要：
We set up a generalization of ubiquitous one-parameter families in algebraic geometry and their use for stability theories ([GIT, HL, AHLH]) to families over toric varieties and their analytic analogues. The language allows us to reformulate degenerations of ``irrational" direction in the literature as canonical objects in a unified manner. Accordingly, we generalize the (semi)stable reduction-type theorem for $Θ$-stratification in [AHLH] of Langton type to our higher rank setup. We also establish a complex analytic analogue of the results. As an infinitesimal analogue of toric spectrum, we also use Novikov type rings, as they provide greater canonicity, but their use can be avoided logically for readers who prefer not to use such rings. Our other papers discuss applications of our framework and the main theorems to problems around K-stability and Kahler geometry.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
