Enriques曲面上Bridgeland模空间的射影性与双有理几何
Projectivity and Birational Geometry of Bridgeland Moduli spaces on an Enriques Surface
摘要：
在一般Bridgeland稳定性条件下，构造了Enriques曲面上半稳定物体的模空间，并证明了它们的射影性.我们进一步推广了经典的关于Enriques曲面上半稳定层的模空间的结果到Bridgeland对应的结果。本文利用Bayer和Macrande构造的随稳定性条件变化的自然nef因子，系统地研究了Bridgeland稳定流形上的跨壁性与这些模空间的极小模型程序之间的关系.我们给出了我们的机器的三个应用，以获得关于Gieseker稳定层的经典模空间的新信息：1）我们获得了Gieseker稳定层的模空间的充分锥中的一个区域，该区域适用于所有非结点Enriques曲面。2)利用半锥的经典几何和Cossec-Dolgachev $ϕ$ -函数，确定了非结点Enriques曲面上$n$点的Hilbert格式的nef锥. 3)我们恢复了Enriques曲面上线性系的一些经典结果，并得到了关于$n$ -非常充分线丛的一些新结果.
英文摘要：
We construct moduli spaces of semistable objects on an Enriques surface for generic Bridgeland stability condition and prove their projectivity. We further generalize classical results about moduli spaces of semistable sheaves on an Enriques surface to their Bridgeland counterparts. Using Bayer and Macrì's construction of a natural nef divisor varying with the stability condition, we begin a systematic exploration of the relation between wall-crossing on the Bridgeland stability manifold and the minimal model program for these moduli spaces. We give three applications of our machinery to obtain new information about the classical moduli spaces of Gieseker-stable sheaves: 1) We obtain a region in the ample cone of the moduli space of Gieseker-stable sheaves which works for all unnodal Enriques surfaces. 2) We determine the nef cone of the Hilbert scheme of $n$ points on an unnodal Enriques surface in terms of the classical geometry of its half-pencils and the Cossec-Dolgachev $ϕ$-function. 3) We recover some classical results on linear systems on Enriques surfaces and obtain some new ones about $n$-very ample line bundles.
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