Volume 25, issue 5 (2021)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 25
Issue 5, 2167–2711
Issue 4, 1631–2166
Issue 3, 1087–1630
Issue 2, 547–1085
Issue 1, 1–546

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
On the vanishing topology of isolated Cohen–Macaulay codimension $2$ singularities

Anne Frühbis-Krüger and Matthias Zach

Geometry & Topology 25 (2021) 2167–2194
Bibliography
1 M Artin, Algebraic construction of Brieskorn’s resolutions, J. Algebra 29 (1974) 330 MR354665
2 J Damon, B Pike, Solvable groups, free divisors and nonisolated matrix singularities, II : Vanishing topology, Geom. Topol. 18 (2014) 911 MR3190605
3 W Decker, G M Greuel, G Pfister, H Schönemann, Singular: a computer algebra system for polynomial computations (2019)
4 D Eisenbud, Commutative algebra: with a view toward algebraic geometry, 150, Springer (1995) MR1322960
5 A Frühbis-Krüger, Classification of simple space curve singularities, Comm. Algebra 27 (1999) 3993 MR1700205
6 A Frühbis-Krüger, On discriminants, Tjurina modifications and the geometry of determinantal singularities, Topol. Appl. 234 (2018) 375 MR3739478
7 A Frühbis-Krüger, A Neumer, Simple Cohen–Macaulay codimension 2 singularities, Comm. Algebra 38 (2010) 454 MR2598893
8 T Gaffney, A Rangachev, Pairs of modules and determinantal isolated singularities, preprint (2014) arXiv:1501.00201
9 S G Gindikin, G M Khenkin, editors, Several complex variables, IV : Algebraic aspects of complex analysis, 10, Springer (1990) MR1042760
10 M Giusti, Classification des singularités isolées simples d’intersections complètes, from: "Singularities, I" (editor P Orlik), Proc. Sympos. Pure Math. 40, Amer. Math. Soc. (1983) 457 MR713086
11 V Goryunov, D Mond, Tjurina and Milnor numbers of matrix singularities, J. Lond. Math. Soc. 72 (2005) 205 MR2145736
12 H Grauert, Über die Deformation isolierter Singularitäten analytischer Mengen, Invent. Math. 15 (1972) 171 MR293127
13 H Grauert, T Peternell, R Remmert, editors, Several complex variables, VII : Sheaf-theoretical methods in complex analysis, 74, Springer (1994) MR1326617
14 G M Greuel, J Steenbrink, On the topology of smoothable singularities, from: "Singularities, I" (editor P Orlik), Proc. Sympos. Pure Math. 40, Amer. Math. Soc. (1983) 535 MR713090
15 S M Gusein-Zade, W Ebeling, On the indices of 1–forms on determinantal singularities, Tr. Mat. Inst. Steklova 267 (2009) 119 MR2723944
16 H Hamm, Lokale topologische Eigenschaften komplexer Räume, Math. Ann. 191 (1971) 235 MR286143
17 R Hartshorne, Deformation theory, 257, Springer (2010) MR2583634
18 S Lojasiewicz, Triangulation of semi-analytic sets, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 18 (1964) 449 MR173265
19 E Looijenga, J Steenbrink, Milnor number and Tjurina number of complete intersections, Math. Ann. 271 (1985) 121 MR779609
20 J Milnor, Singular points of complex hypersurfaces, 61, Princeton Univ. Press (1968) MR0239612
21 H Møller Pedersen, On Tjurina transform and resolution of determinantal singularities, preprint (2016) arXiv:1604.06029
22 D Mond, D van Straten, Milnor number equals Tjurina number for functions on space curves, J. Lond. Math. Soc. 63 (2001) 177 MR1802765
23 T Okuma, Numerical Gorenstein elliptic singularities, Math. Z. 249 (2005) 31 MR2106969
24 O Riemenschneider, Familien komplexer Räume mit streng pseudokonvexer spezieller Faser, Comment. Math. Helv. 51 (1976) 547 MR437808
25 K Saito, Quasihomogene isolierte Singularitäten von Hyperflächen, Invent. Math. 14 (1971) 123 MR294699
26 M Schaps, Nonsingular deformations of a determinantal scheme, Pacific J. Math. 65 (1976) 209 MR422269
27 M Schaps, Deformations of Cohen–Macaulay schemes of codimension 2 and non-singular deformations of space curves, Amer. J. Math. 99 (1977) 669 MR491715
28 D van Straten, Weakly normal surface singularities and their improvements, PhD thesis, Universiteit Leiden (1987)
29 G N Tyurina, Absolute isolatedness of rational singularities and triple rational points, Funkcional. Anal. i Priložen. 2 (1968) 70 MR0245830
30 J M Wahl, Equations defining rational singularities, Ann. Sci. École Norm. Sup. 10 (1977) 231 MR444655
31 J M Wahl, Simultaneous resolution of rational singularities, Compos. Math. 38 (1979) 43 MR523262
32 J Wahl, Milnor and Tjurina numbers for smoothings of surface singularities, Algebr. Geom. 2 (2015) 315 MR3370125
33 M Zach, An observation concerning the vanishing topology of certain isolated determinantal singularities, Math. Z. 291 (2019) 1263 MR3936107