AI 中文总结
本文研究布里奇兰德稳定流形上整体维数函数的可达性与边界行为，证明了n维光滑射影簇上该函数下确界为n，推广了可达性结果，构造了光滑射影曲线约化稳定空间的紧化并讨论了相关代数模型。
AI 中文摘要
本文研究布里奇兰德（Bridgeland）稳定流形上整体维数函数的可达性与边界行为。对于n维光滑射影簇X，我们证明整体维数函数的下确界为n：当-K_X丰富时该值可达；当K_X属于Pic⁰(X)时，每个稳定条件都取该值；当K_X大且内省时该值不可达。我们还将这些可达性结果推广到预稳定条件。此外，我们构造了光滑射影曲线约化稳定空间的紧化，使整体维数函数可连续延拓至该紧化空间。最后，我们讨论了可达性问题的代数模型，包括有限维代数与半正交分解。
英文摘要
In this paper, we study the reachability and boundary behavior of the global dimension function on Bridgeland stability manifolds. For a smooth projective variety $X$ of dimension $n$, we prove that the infimum of the global dimension function is $n$. This value is attained when $-K_X$ is ample, is taken by every stability condition when $K_X\in\mathrm{Pic}^0(X)$, and is not attained when $K_X$ is big and nef. We also extend these reachability results to pre-stability conditions. In addition, we construct compactifications of reduced stability spaces of smooth projective curves to which the global dimension function extends continuously. Finally, we discuss algebraic models of the reachability problem, including finite-dimensional algebras and semiorthogonal decompositions.
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