Details
| Original language | English |
|---|---|
| Pages (from-to) | 1263-1293 |
| Number of pages | 31 |
| Journal | Mathematische Zeitschrift |
| Volume | 291 |
| Issue number | 3-4 |
| Early online date | 15 Oct 2018 |
| Publication status | Published - 1 Apr 2019 |
Abstract
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In: Mathematische Zeitschrift, Vol. 291, No. 3-4, 01.04.2019, p. 1263-1293.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - An observation concerning the vanishing topology of certain isolated determinantal singularities
AU - Zach, Matthias Pablo
N1 - Funding information: The author wishes to thank A. Frühbis-Krüger for guidance and support, M. Tib?ar for discussions during a visit in Hannover and the organization of the workshop on nonisolated singularities in Lille and D. Siersma for further discussions on the topic. Furthermore, he thanks M.A.S. Ruas and the ICMC for hospitality and a stimulating mathematical framework during a stay at the USP in São Carlos. Thanks also for conversations with T. Gaffney and M.A.S. Ruas on determinantal singularities, which significantly broadened the viewpoint of this paper. During the preparation of this article, the author was funded by the DFG program GRK 1463 and the DAAD program IP@Leibniz at the Leibniz Universität Hannover.
PY - 2019/4/1
Y1 - 2019/4/1
N2 - We extend the results about the vanishing topology of isolated Cohen–Macaulay codimension 2 singularities from a previous article by Frühbis-Krüger and Zach (On the vanishing topology of isolated Cohen–Macaulay codimension 2 singularities. arXiv:1501.01915, 2015). Due to the Hilbert–Burch theorem, these singularities have a canonical determinantal structure and a well behaved deformation theory, which, in particular, yields a unique Milnor fiber. Studying the case of possibly non-isolated singularities in the Tjurina transform, as introduced in Frühbis-Krüger and Zach (2015), we reveal that in dimension 3 and 2 there is always exactly one special vanishing cycle in degree 2 closely related to the determinantal structure of the singularity.
AB - We extend the results about the vanishing topology of isolated Cohen–Macaulay codimension 2 singularities from a previous article by Frühbis-Krüger and Zach (On the vanishing topology of isolated Cohen–Macaulay codimension 2 singularities. arXiv:1501.01915, 2015). Due to the Hilbert–Burch theorem, these singularities have a canonical determinantal structure and a well behaved deformation theory, which, in particular, yields a unique Milnor fiber. Studying the case of possibly non-isolated singularities in the Tjurina transform, as introduced in Frühbis-Krüger and Zach (2015), we reveal that in dimension 3 and 2 there is always exactly one special vanishing cycle in degree 2 closely related to the determinantal structure of the singularity.
UR - http://www.scopus.com/inward/record.url?scp=85064038636&partnerID=8YFLogxK
U2 - 10.1007/s00209-018-2143-9
DO - 10.1007/s00209-018-2143-9
M3 - Article
AN - SCOPUS:85064038636
VL - 291
SP - 1263
EP - 1293
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
SN - 0025-5874
IS - 3-4
ER -