Moduli of vector bundles on projective surfaces: some basic results
Moduli of vector bundles on projective surfaces: some basic results
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投影面上向量束的模：一些基本结果
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发表时间：
1994
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通讯作者：
K. O’Grady
中科院分区：
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作者：
K. O’Grady
证明了在射影光滑复表面上无扭轮轴的模空间是不可约的、约简的，且在期望维数足够大的条件下具有期望维数。实际上我们证明了更多：给定曲面上的一个线束，我们证明了具有非零扭曲（由所选的线束）自同态的轴的模数的增长速度慢于模空间的期望维数（对于定秩和递增判别）。我们得到的边界是有效的：我们集中在秩2的情况下，我们给出了判别的下界，保证了模空间的期望维数被缩减。我们还给出了完全交的一个有效的不可约性结果。所有这些都是从模空间中不与边界相交的完全子集的维数限定定理推导出来的。
We prove that moduli spaces of torsion-free sheaves on a projective smooth complex surface are irreducible, reduced and of the expected dimension, provided the expected dimension is large enough. Actually we prove more: given a line bundle on the surface, we show that the number of moduli of sheaves which have a non-zero twisted (by the chosen line-bundle) endomorphism grows slower than the expected dimension of the moduli space (for fixed rank and increasing discriminant). The bounds we get are effective: we concentrate on the case of rank two and we give a lower bound on the discriminant guaranteeing that the moduli space is reduced of the expected dimension. We also give an effective irreducibility result for complete intersections. All of the above follows from a theorem bounding the dimension of complete subsets of the moduli space which do not intersect the boundary.