论文标题
符号Lefschetz振动和合理排列的地理
Geography of symplectic Lefschetz fibrations and rational blowdowns
论文作者
论文摘要
我们产生简单的连接，最小的，符号的Lefschetz纤维，以实现Noether线下方的象征地理平面中的所有晶格点。这提供了具有霍明型Lefschetz纤维化的复杂地理平面的古典作品的符合性扩展。我们的示例是通过合理地用簇状的淋巴结纤维来理性地吹干Lefschetz纤维的，其总空间可能是新的同型椭圆表面。同样，在标准有理表面上较高属的Lefschetz纤维上的群集淋巴结纤维，我们获得了理性的排列配置，这些配置产生了小型象征性异国情调的新结构，$ 4 $ - manifolds。我们提供了一个最小符号外来的$ \ mathbb {cp} \＃5 \，\ edimelline {\ mathbb {cp}} $通过此过程应用于属 - $ 3 $纤维化的示例。
We produce simply connected, minimal, symplectic Lefschetz fibrations realizing all the lattice points in the symplectic geography plane below the Noether line. This provides a symplectic extension of the classical works populating the complex geography plane with holomorphic Lefschetz fibrations. Our examples are obtained by rationally blowing down Lefschetz fibrations with clustered nodal fibers, the total spaces of which are potentially new homotopy elliptic surfaces. Similarly, clustering nodal fibers on higher genera Lefschetz fibrations on standard rational surfaces, we get rational blowdown configurations that yield new constructions of small symplectic exotic $4$-manifolds. We present an example of a construction of a minimal symplectic exotic $\mathbb{CP} \# 5\,\overline{\mathbb{CP}}$ through this procedure applied to a genus-$3$ fibration.
