论文标题
椭圆表面上的可半固定的希格斯捆
Semistable Higgs bundles on elliptic surfaces
论文作者
论文摘要
我们分析了一类椭圆形表面上的higgs捆绑$（v，ϕ）$π：x \ to b $，其基础向量束$ v $具有垂直决定符，并且可以半固定。我们证明，如果$ v $的光谱曲线减少了，则$ ϕ $是垂直的，而如果$ v $是光纤定期的，则降低（分别是积分）频谱曲线，并且其排名和第二个Chern数量满足涉及$ b $的属的不平等，然后是$ b $的属性，然后是$ undle $π$（如果是$π$），则是undectal undlede undlede undlede unde usp。标量。我们将这些结果应用于表征可斜坡的希格斯捆绑的问题，这些斜率捆绑了判别性，从而通过其下拉的可分离性通过地图从任意（平滑，不可减少，完整）曲线到$ x $来表征其背书的准性。
We analyze Higgs bundles $(V,ϕ)$ on a class of elliptic surfaces $π:X\to B$, whose underlying vector bundle $V$ has vertical determinant and is fiberwise semistable. We prove that if the spectral curve of $V$ is reduced, then $ϕ$ is vertical, while if $V$ is fiberwise regular with reduced (resp. integral) spectral curve, and if its rank and second Chern number satisfy an inequality involving the genus of $B$ and the degree of the fundamental line bundle of $π$ (resp., if the fundamental line bundle is sufficiently ample), then $ϕ$ is scalar. We apply these results to the problem of characterizing slope-semistable Higgs bundles with vanishing discriminant in terms of the semistability of their pull-backs via maps from arbitrary (smooth, irreducible, complete) curves to $X$.
