Volume 18:
Special volume in honor of the life and mathematics of
Egbert Brieskorn

Contents

Preface i
Editors: Gert-Martin Greuel, Helmut A. Hamm, Lê Dũng Tráng

Part 0: History

Life and work of Egbert Brieskorn (1936-2013) 1
Gert-Martin Greuel and Walter Purkert

Singularities and Polyhedra 29
Egbert Brieskorn

Singularities and Exotic Spheres 35
Friedrich Hirzebruch

Part I: Analytic Methods

On the b-exponents of generic isolated plane curve singularities 36
E. Artal Bartolo, Pi. Cassou-Noguès, I. Luengo, and A. Melle-Hernández

The Sheaf 50
Daniel Barlet

Brieskorn and the monodromy 84
Jean-Paul Brasselet and Marcos Sebastiani

Foliations by curves uniquely determined by minimal subschemes of its singularities 105
Antonio Campillo and Jorge Olivares

On 1-forms on isolated complete intersection curve singularities 114
Alexandru Dimca and Gert-Martin Greuel

μ-constant monodromy groups and Torelli results for the quadrangle singularities and the bimodal series 119
Falko Gauss and Claus Hertling

Picard groups for line bundles with connections 215
Helmut A. Hamm and Lê Dũng Tráng

Some properties and applications of Brieskorn lattices 238
Claude Sabbah

On the structure of Brieskorn lattices, II 248
Morihiko Saito

A residual duality over Gorenstein rings with application to logarithmic differential forms 272
Mathias Schulze and Laura Tozzo

Part II: Topology and Real Singularities

A zoo of geometric homology theories 300
Matthias Kreck

Morsifications of real plane curve singularities 307
Peter Leviant and Eugenii Shustin

Smooth mixed projective curves and a conjecture 329
Mutsuo Oka

Lacunas and local algebraicity of volume functions 350
V. A. Vassiliev

Part III: Algebraic Methods and Algebraic Geometry

Schubert Decomposition for Milnor Fibers of the Varieties of Singular Matrices 358
James Damon

A McKay correspondence for the Poincaré series of some finite subgroups of SL_3(C) 397
Wolfgang Ebeling

Accuracy of noisy Spike-Train Reconstruction: a Singularity Theory point of view 409
Gil Goldman, Yehonatan Salman, and Yosef Yomdin

Noncommutative Deformations of Thick Points 427
Olav Arnfinn Laudal

Strata of discriminantal arrangements 440
Anatoly Libgober and Simona Settepanella

On a discriminant knot group problem of Brieskorn 455
Michael Lönne

Linear subspace arrangements associated with normal surface singularities 464
András Némethi

Kulikov singularities 477
Jan Stevens

Remarks on the Gaudin model modulo p 486
Alexander Varchenko