Unchaining surgery and topology of symplectic 4-manifolds
Unchaining surgery and topology of symplectic 4-manifolds
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DOI：
10.1007/s00209-023-03204-x
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发表时间：
2019-03
影响因子：
0.8
通讯作者：
R. Baykur;Kenta Hayano;Naoyuki Monden
中科院分区：
文献类型：
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作者：
R. Baykur;Kenta Hayano;Naoyuki Monden
我们研究了一种辛外科手术，我们称之为链式手术，它有效地减少了第二Betti数和辛科代拉维数在同一时间。使用unchaining，我们给出了新的构造辛Calabi-Yau曲面从复杂的曲面的一般类型，并完全解决了一个猜想的Stipsicz的存在例外部分的Lefschetz纤维化。结合unchaining手术与其他人，这都对应于某些monodromy替代Lefschetz铅笔，我们提供了进一步的应用，如新的结构的奇异辛4-流形，和不等价的铅笔相同的属和相同数量的基点上的家庭辛4-流形。同时，我们给出了一个由单值性判断铅笔的全空间是否为自旋的简便判据。
We study a symplectic surgery operation we callunchaining, which effectively reduces the second Betti number and the symplectic Kodaira dimension at the same time. Using unchaining, we give novel constructions of symplectic Calabi–Yau surfaces from complex surfaces of general type and completely resolve a conjecture of Stipsicz on the existence of exceptional sections in Lefschetz fibrations. Combining the unchaining surgery with others, which all correspond to certain monodromy substitutions for Lefschetz pencils, we provide further applications, such as new constructions of exotic symplectic 4-manifolds, and inequivalent pencils of the same genera and the same number of base points on families of symplectic 4-manifolds. Meanwhile, we present a handy criterion for determining from the monodromy of a pencil whether its total space is spin or not.