Details
| Original language | English |
|---|---|
| Publication status | E-pub ahead of print - 5 Jul 2021 |
Abstract
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2021.
Research output: Working paper/Preprint › Preprint
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TY - UNPB
T1 - On the topology of determinantal links
AU - Zach, Matthias
N1 - 41 pages, 7 tables
PY - 2021/7/5
Y1 - 2021/7/5
N2 - We study the cohomology of the generic determinantal varieties \( M_{m,n}^s = \{ \varphi \in \mathbb C^{m\times n} : \mathrm{rank} \varphi <s \} \), their polar multiplicities, their sections \( Dk∩Msm,n \) by generic hyperplanes \( Dk \) of various dimension \(k\), and the real and complex links of the spaces \( (Dk∩Msm,n,0) \). Such complex links were shown to provide the basic building blocks in a bouquet decomposition for the (determinantal) smoothings of smoothable isolated determinantal singularities. The detailed vanishing topology of such singularities was still not fully understood beyond isolated complete intersections and a few further special cases. Our results now allow to compute all distinct Betti numbers of any determinantal smoothing.
AB - We study the cohomology of the generic determinantal varieties \( M_{m,n}^s = \{ \varphi \in \mathbb C^{m\times n} : \mathrm{rank} \varphi <s \} \), their polar multiplicities, their sections \( Dk∩Msm,n \) by generic hyperplanes \( Dk \) of various dimension \(k\), and the real and complex links of the spaces \( (Dk∩Msm,n,0) \). Such complex links were shown to provide the basic building blocks in a bouquet decomposition for the (determinantal) smoothings of smoothable isolated determinantal singularities. The detailed vanishing topology of such singularities was still not fully understood beyond isolated complete intersections and a few further special cases. Our results now allow to compute all distinct Betti numbers of any determinantal smoothing.
M3 - Preprint
BT - On the topology of determinantal links
ER -