Singularities in Geometry and Topology Strasbourg 2009 / [electronic resource] :
Vincent Blanlœil, Toru Ohmoto
- Zuerich, Switzerland : European Mathematical Society Publishing House, 2012
- 1 online resource (370 pages)
- IRMA Lectures in Mathematics and Theoretical Physics (IRMA) 20 .
Optical caustics and their modelling as singularities / On local equisingularity / Jet schemes of homogeneous hypersurfaces / Singularities in relativity / On the universal degenerating family of Riemann surfaces / Algebraic local cohomologies and local $b$-functions attached to semiquasihomogeneous singularities with $L(f)=2$ / A note on the Chern–Schwartz–MacPherson class / On mixed projective curves / Invariants of splice quotient singularities / A note on the toric duality between the cyclic quotient surface singularities $A_$ and $A_$ / Nearby cycles and characteristic classes of singular spaces / Residues of singular holomorphic distributions / Two birational invariants in statistical learning theory / Frobenius morphisms of noncommutative blowups / Bivariant motivic Hirzebruch class and a zeta function of motivic Hirzebruch class / Minimality of hyperplane arrangements and basis of local system cohomology / Alain Joets -- Helmut A. Hamm -- Shihoko Ishii, Akiyoshi Sannai, Kei-ichi Watanabe -- Tatsuhiko Koike -- Yukio Matsumoto -- Yayoi Nakamura, Shinichi Tajima -- Toru Ohmoto -- Mutsuo Oka -- Tomohiro Okuma -- Oswald Riemenschneider -- Jörg Schürmann -- Tatsuo Suwa -- Sumio Watanabe -- Takehiko Yasuda -- Shoji Yokura -- Masahiko Yoshinaga.
Restricted to subscribers: http://www.ems-ph.org/ebooks.php
This volume arises from 5th Franco-Japanese Symposium on Singularities, held in Strasbourg in August 2009. The conference brought together an international group of researchers working on singularities in algebraic geometry, analytic geometry and topology, mainly from France and Japan. Besides, it also organized a special session, JSPS Forum on Singularities and Applications, which was aimed to introduce some recent applications of singularity theory to physics and statistics. This book comprises research papers and short lecture notes on advanced topics on singularities. Some surveys on applications that were presented in the Forum are also added. Topics covered include splice surface singularities, b-functions, equisingularity, degenerating families of Riemann surfaces, hyperplane arrangements, mixed singularities, jet schemes, noncommutative blow-ups, characteristic classes of singular spaces, and applications to geometric optics, cosmology and learning theory. Graduate students who wish to learn about various approaches to singularities, as well as experts in the field and researchers in other areas of mathematics and science will find the contributions to this volume a rich source for further study and research.
9783037196182
10.4171/118 doi
Algebraic geometry
Algebraic geometry
Several complex variables and analytic spaces
Manifolds and cell complexes
Global analysis, analysis on manifolds
Optical caustics and their modelling as singularities / On local equisingularity / Jet schemes of homogeneous hypersurfaces / Singularities in relativity / On the universal degenerating family of Riemann surfaces / Algebraic local cohomologies and local $b$-functions attached to semiquasihomogeneous singularities with $L(f)=2$ / A note on the Chern–Schwartz–MacPherson class / On mixed projective curves / Invariants of splice quotient singularities / A note on the toric duality between the cyclic quotient surface singularities $A_$ and $A_$ / Nearby cycles and characteristic classes of singular spaces / Residues of singular holomorphic distributions / Two birational invariants in statistical learning theory / Frobenius morphisms of noncommutative blowups / Bivariant motivic Hirzebruch class and a zeta function of motivic Hirzebruch class / Minimality of hyperplane arrangements and basis of local system cohomology / Alain Joets -- Helmut A. Hamm -- Shihoko Ishii, Akiyoshi Sannai, Kei-ichi Watanabe -- Tatsuhiko Koike -- Yukio Matsumoto -- Yayoi Nakamura, Shinichi Tajima -- Toru Ohmoto -- Mutsuo Oka -- Tomohiro Okuma -- Oswald Riemenschneider -- Jörg Schürmann -- Tatsuo Suwa -- Sumio Watanabe -- Takehiko Yasuda -- Shoji Yokura -- Masahiko Yoshinaga.
Restricted to subscribers: http://www.ems-ph.org/ebooks.php
This volume arises from 5th Franco-Japanese Symposium on Singularities, held in Strasbourg in August 2009. The conference brought together an international group of researchers working on singularities in algebraic geometry, analytic geometry and topology, mainly from France and Japan. Besides, it also organized a special session, JSPS Forum on Singularities and Applications, which was aimed to introduce some recent applications of singularity theory to physics and statistics. This book comprises research papers and short lecture notes on advanced topics on singularities. Some surveys on applications that were presented in the Forum are also added. Topics covered include splice surface singularities, b-functions, equisingularity, degenerating families of Riemann surfaces, hyperplane arrangements, mixed singularities, jet schemes, noncommutative blow-ups, characteristic classes of singular spaces, and applications to geometric optics, cosmology and learning theory. Graduate students who wish to learn about various approaches to singularities, as well as experts in the field and researchers in other areas of mathematics and science will find the contributions to this volume a rich source for further study and research.
9783037196182
10.4171/118 doi
Algebraic geometry
Algebraic geometry
Several complex variables and analytic spaces
Manifolds and cell complexes
Global analysis, analysis on manifolds