J-可嵌入可约曲面（放大版）
J-embeddable reducible surfaces (enlarged version)
摘要：
设V是P^n（C）中的一个簇，W是P^n中的一个维数为w的线性空间。我们说V可以同构地投影到W上，如果存在一个线性投影f，从一个与W不相交的合适的线性空间L，dim（L）= n-w-1 >= 0，使得f（V）同构于V。W.约翰逊：投射簇的浸入和嵌入，Acta Math. [140]（1981）49-74）如果f'是内射的，并且f'的微分是有限映射。本文对J-可嵌入可约曲面进行了分类，等价地，对割线簇维数不超过4的可约曲面进行了分类。对于具有两个组件的曲面，分类非常详细。对于三个或更多的组件，我们给出了一个合理的分类，考虑到完整的分类是非常丰富的情况下，subcase和subsubcase。
英文摘要：
Let V be a variety in P^n(C) and let W be a linear space, of dimension w, in P^n. We say that V can be isomorphically projected onto W if there exists a linear projection f, from a suitable linear space L disjoint from W, dim(L) = n-w-1 >= 0, such that f(V) is isomorphic to V. Let f' be the restriction of f to V. We say that f' is a J-embedding of V (see K. W. Johnson: Immersion and embedding of projective varieties, Acta Math. [140] (1981) 49-74) if f' is injective and the differential of f' is a finite map. In this paper we classify the J-embeddable reducible surfaces, equivalently, the reducible surfaces whose secant variety has dimension at most 4. The classification is very detailed for surfaces having two components. For three or more components we give a reasonable classification, taking into account that the complete classification is very rich of cases, subcases and subsubcases.
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