射影空间中刚性完全交的自同构群
Automorphism groups of rigid complete intersections
AI总结：
研究射影空间中次数严格递增的超曲面完全交的自同构群，利用组合刚性条件证明其自同构群是定义超曲面自同构群的交集，并应用此原理于两个超曲面完全交的自然族，确定了相关自同构群。
AI中文摘要：
我们研究射影空间中次数严格递增的超曲面完全交的自同构群。在定义多项式元组的组合刚性条件下，我们证明完全交的每个自同构可扩展为每个定义超曲面的自同构，其自同构群是定义超曲面自同构群的交集。我们将此原理应用于两个不同次数的两个超曲面完全交的自然族。对于两个费马超曲面的完全交，我们确定了每个光滑情形下的自同构群。对于一个克莱因超曲面与逆序克莱因超曲面的完全交，在两个次数的显式算术条件下描述了自同构群，瓦格斯塔夫型克莱因超曲面是自然的例子来源。
英文摘要：
We study the automorphism groups of complete intersections of hypersurfaces of strictly increasing degrees in projective space. Under a combinatorial rigidity condition on the tuple of defining polynomials, we show that every automorphism of the complete intersection extends to an automorphism of each defining hypersurface, so that its automorphism group is the intersection of the automorphism groups of the defining hypersurfaces. We apply this principle to two natural families of complete intersections of two hypersurfaces of different degrees. For complete intersections of two Fermat hypersurfaces, we determine the automorphism group in every smooth case. For complete intersections of a Klein hypersurface with the reverse-order Klein hypersurface, we describe the automorphism group under an explicit arithmetic condition relating the two degrees, with Klein hypersurfaces of Wagstaff type as a natural source of examples.
