A formula for the Chern classes of symplectic blow‐ups
A formula for the Chern classes of symplectic blow‐ups
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DOI：
10.1112/jlms/jdm061
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发表时间：
2006-01
期刊：
影响因子：
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通讯作者：
H. Geiges;F. Pasquotto
中科院分区：
文献类型：
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作者：
H. Geiges;F. Pasquotto
证明了由Porteous和Lascu-Scott得到的代数簇爆破的陈类(在Chow环上)对辛流形和复流形的爆破(在奇异上同调环上)也成立.这是第二作者在她解决8维辛流形的地理问题时使用的。该证明同样适用于任意流形的实爆破，并给出了相应的Stiefel-Whitney类爆破公式。在论证过程中，证明了交理论中Grothendieck公式的拓扑类比。
It is shown that the formula for the Chern classes (in the Chow ring) of blow‐ups of algebraic varieties, due to Porteous and Lascu–Scott, also holds (in the singular cohomology ring) for blow‐ups of symplectic and complex manifolds. This was used by the second author in her solution of the geography problem for 8‐dimensional symplectic manifolds. The proof equally applies to real blow‐ups of arbitrary manifolds and yields the corresponding blow‐up formula for the Stiefel–Whitney classes. In the course of the argument, the topological analogue of Grothendieck’s formule clef in intersection theory is proved.