Geometry & Topology Volume 18, issue 2 (2014)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

Solvable groups, free divisors and nonisolated matrix singularities II: Vanishing topology

James Damon and Brian Pike

Geometry & Topology 18 (2014) 911–962

DOI: 10.2140/gt.2014.18.911

Bibliography

1	J W Bruce, On families of symmetric matrices, Mosc. Math. J. 3 (2003) 335, 741 MR2025264
2	R O Buchweitz, D Mond, Linear free divisors and quiver representations, from: "Singularities and computer algebra" (editors C Lossen, G Pfister), London Math. Soc. Lecture Note Ser. 324, Cambridge Univ. Press (2006) 41 MR2228227
3	L Burch, On ideals of finite homological dimension in local rings, Proc. Cambridge Philos. Soc. 64 (1968) 941 MR0229634
4	J Damon, The unfolding and determinacy theorems for subgroups of $\mathcal{A}$ and $\mathcal{K}$, Mem. Amer. Math. Soc. 306, AMS (1984) MR748971
5	J Damon, Deformations of sections of singularities and Gorenstein surface singularities, Amer. J. Math. 109 (1987) 695 MR900036
6	J Damon, A Bezout theorem for determinantal modules, Compositio Math. 98 (1995) 117 MR1354264
7	J Damon, Higher multiplicities and almost free divisors and complete intersections, Mem. Amer. Math. Soc. 589, AMS (1996) MR1346928
8	J Damon, Nonlinear sections of nonisolated complete intersections, from: "New developments in singularity theory" (editors D Siersma, C T C Wall, V Zakalyukin), NATO Sci. Ser. II Math. Phys. Chem. 21, Kluwer Acad. Publ. (2001) 405 MR1849318
9	J Damon, D Mond, $\mathcal{A}$–codimension and the vanishing topology of discriminants, Invent. Math. 106 (1991) 217 MR1128213
10	J Damon, B Pike, Solvable groups, free divisors and nonisolated matrix singularities I: Towers of free divisors arXiv:1201.1577
11	A Frühbis-Krüger, Classification of simple space curve singularities, Comm. Algebra 27 (1999) 3993 MR1700205
12	A Frühbis-Krüger, A Neumer, Simple Cohen–Macaulay codimension $2$ singularities, Comm. Algebra 38 (2010) 454 MR2598893
13	J J Gervais, Germes de $G$–détermination finie, C. R. Acad. Sci. Paris Sér. A–B 284 (1977) MR0440595
14	J J Gervais, Critères de $G$–stabilité en termes de transversalité, Canad. J. Math. 31 (1979) 264 MR528804
15	V Goryunov, D Mond, Tjurina and Milnor numbers of matrix singularities, J. London Math. Soc. 72 (2005) 205 MR2145736
16	M Granger, D Mond, A Nieto-Reyes, M Schulze, Linear free divisors and the global logarithmic comparison theorem, Ann. Inst. Fourier (Grenoble) 59 (2009) 811 MR2521436
17	D R Grayson, M E Stillman, Macaulay2, a software system for research in algebraic geometry
18	G M Greuel, Dualität in der lokalen Kohomologie isolierter Singularitäten, Math. Ann. 250 (1980) 157 MR582515
19	G M Greuel, D T Lê, Spitzen, Doppelpunkte und vertikale Tangenten in der Diskriminante verseller Deformationen von vollständigen Durchschnitten, Math. Ann. 222 (1976) 71 MR0441961
20	G M Greuel, J Steenbrink, On the topology of smoothable singularities, from: "Singularities, Part 1" (editor P Orlik), Proc. Sympos. Pure Math. 40, Amer. Math. Soc. (1983) 535 MR713090
21	T H Gulliksen, O G Negård, Un complexe résolvant pour certains idéaux déterminantiels, C. R. Acad. Sci. Paris Sér. A-B 274 (1972) MR0296063
22	D Hilbert, Ueber die Theorie der algebraischen Formen, Math. Ann. 36 (1890) 473 MR1510634
23	T Józefiak, Ideals generated by minors of a symmetric matrix, Comment. Math. Helv. 53 (1978) 595 MR511849
24	T Józefiak, P Pragacz, Ideals generated by Pfaffians, J. Algebra 61 (1979) 189 MR554859
25	M Kato, Y Matsumoto, On the connectivity of the Milnor fiber of a holomorphic function at a critical point, from: "Manifolds" (editors A Hattori, N Sūgakkai), Univ. Tokyo Press (1975) 131 MR0372880
26	D T Lê, B Teissier, Cycles evanescents, sections planes et conditions de Whitney, II, from: "Singularities, Part 2", Proc. Sympos. Pure Math. 40, Amer. Math. Soc. (1983) 65 MR713238
27	E J N Looijenga, Isolated singular points on complete intersections, London Mathematical Society Lecture Note Series 77, Cambridge Univ. Press (1984) MR747303
28	E Looijenga, J Steenbrink, Milnor number and Tjurina number of complete intersections, Math. Ann. 271 (1985) 121 MR779609
29	M d S Pereira, Determinantal varieties and singularities of matrices, PhD thesis, University of São Paulo (2010)
30	B Pike, VectorFields 1.0 and calc\_smn 1.0: Macaulay2 programs
31	B Pike, Singular Milnor numbers for nonisolated matrix singularities, PhD thesis, University of North Carolina (2010) MR2782347
32	K Saito, Theory of logarithmic differential forms and logarithmic vector fields, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 27 (1980) 265 MR586450
33	M Schaps, Deformations of Cohen–Macaulay schemes of codimension $2$ and nonsingular deformations of space curves, Amer. J. Math. 99 (1977) 669 MR0491715
34	B Teissier, Cycles évanescents, sections planes et conditions de Whitney, from: "Singularités à Cargèse", Astérisque 7–8, Soc. Math. France (1973) 285 MR0374482
35	G N Tjurina, Absolute isolation of rational singularities, and triple rational points, Funkcional. Anal. i Priložen. 2 (1968) 70 MR0245830
36	J Wahl, Smoothings of normal surface singularities, Topology 20 (1981) 219 MR608599