论文标题
颤抖和颤抖的基因座的平等
Equality of the wobbly and shaky loci
论文作者
论文摘要
令$ x $为属$ g \ geq 2 $的平滑复杂的投影曲线。我们证明，$ x $上的$ x $上的抛物线矢量捆绑$ \ Mathcal {e} $是（非常）摇晃的，即$ \ $ \ Mathcal {e} $具有非零（强烈的）抛物面的抛物面nilpotent nilpotent nilpotent higgs field，并且仅在（强烈）（强度）的情况下，它是正确的。从（强）抛物线Higgs模量到抛物线束模量空间的理性图，都假定为光滑。这解决了Donagi-Pantev [DP1]在抛物线和矢量束上下文中的猜想。为此，我们证明了非常稳定的抛物线束的稳定性，以及抛物线束非常稳定的标准。
Let $X$ be a smooth complex projective curve of genus $g\geq 2$. We prove that a parabolic vector bundle $\mathcal{E}$ on $X$ on $X$ is (strongly) wobbly, i.e. $\mathcal{E}$ has a non-zero (strongly) parabolic nilpotent Higgs field, if and only if it is (strongly) shaky, i.e., it is in the image of the exceptional divisor of a suitable resolution of the rational map from the (strongly) parabolic Higgs moduli to the parabolic bundle moduli space, both assumed to be smooth. This solves a conjecture by Donagi-Pantev [DP1] in the parabolic and the vector bundle context. To this end, we prove the stability of strongly very stable parabolic bundles, and criteria for very stability of parabolic bundles.
