论文标题
同骨log calabi-yau除数和几乎要复曲面的枚举方面
Enumerative aspect of symplectic log Calabi-Yau divisors and almost toric fibrations
论文作者
论文摘要
在本文中，我们对固定符号合理表面中的sybletic log calabi-yau除数的同位素类别感兴趣。我们给出了几个等效的定义，并证明了稳定性，有限性和刚性结果。在计算复曲面动作的问题上，我们在$ C_1 $ -NEF锥体的限制性区域中获得了符号日志calabi-yau除数的一般计数公式。在所有符号形式的复杂投影空间的2和3分爆炸的情况下，还给出了详细的计数。在我们的框架中，分析Delzant多边形的组合学的复杂性降低为同源类的布置。然后，我们通过几乎要进行复曲面纤维来研究其关系。我们提出了通过一些几乎要复的纤维纤维来实现所有符合日志calabi-yau除数的问题，并将其与特殊区域中的另一个猜想一起验证。
In this paper we are interested in the isotopy classes of symplectic log Calabi-Yau divisors in a fixed symplectic rational surface. We give several equivalent definitions and prove the stability, finiteness and rigidity results. Motivated by the problem of counting toric actions, we obtain a general counting formula of symplectic log Calabi-Yau divisors in a restrictive region of $c_1$-nef cone. A detailed count in the case of 2- and 3-point blow-ups of complex projective space for all symplectic forms is also given. In our framework the complexity of the combinatorics of analyzing Delzant polygons is reduced to the arrangement of homology classes. Then we study its relation with almost toric fibrations. We raise the problem of realizing all symplectic log Calabi-Yau divisors by some almost toric fibrations and verify it together with another conjecture of Symington in a special region.
