关于全支撑性质的注记
A remark on the full support property
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中文总结 AI 辅助
该研究证明域上射影概型数值预稳定条件的质量-Hom界蕴含全数值Grothendieck群下的支撑性质，结合稳定条件构造得到域上所有射影概型的全支撑稳定条件，还建立相对统一版本并确定稳定流形的典范分支。
中文摘要 AI 辅助
我们证明，域上射影概型数值预稳定条件的质量-Hom界，蕴含其关于全数值Grothendieck群的支撑性质。结合近期射影概型上稳定条件的构造，这给出了域上每个射影概型上具有全支撑性质的稳定条件。我们还在相对情形建立了统一版本。最后，我们证明全数值稳定流形中的特殊分支与极化的选择无关，从而定义了一个典范分支。
英文摘要
We show that a mass-Hom bound for a numerical pre-stability condition on a projective scheme over a field implies the support property with respect to the full numerical Grothendieck group. Combined with the recent construction of stability conditions on projective schemes, this yields stability conditions with full support property on every projective scheme over a field. We also establish a uniform version in the relative setting. Finally, we show that the distinguished component in the full numerical stability manifold is independent of the choice of polarization, thereby defining a canonical component.
