射影复形曲面同调的拉格朗日表示
Representants lagrangiens de l'homologie des surfaces projectives complexes
摘要：
利用Donaldson和Auroux关于伪全纯曲线的结果以及Duval的有理凸性构造，本文研究了复射影曲面中表示2维同调类的光滑Lagrange曲面的存在性。证明了：若射影曲面X是极小的、一般类型的、几何亏格不均匀的，且有一个有效的、光滑的、连通的典范除子K，则在实二维同调群H 2（X）中存在一个非空的凸开锥，使得该锥中每一个整同调类的倍数都可以用X中的嵌入拉格朗日曲面\K表示.一个推论断言这样的曲面X是Kronheimer和Mrowka意义下的简单类型。
英文摘要：
Using results by Donaldson and Auroux on pseudo-holomorphic curves as well as Duval's rational convexity construction, the paper investigates the existence of smooth Lagrangian surfaces representing 2-dimensional homology classes in complex projective surfaces. We prove that if the projective surface X is minimal, of general type, with uneven geometric genus, and has an effective, smooth and connected canonical divisor K, then there exists a non-empty convex open cone in the real 2-dimensional homology group H2(X) such that a multiple of every integral homology class in this cone can be represented by an embedded Lagrangian surface in X\K. A corollary asserts that such a surface X is of simple type in the sense of Kronheimer and Mrowka.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
