scholarly journals Poincaré series and monodromy of a two-dimensional quasihomogeneous hypersurface singularity

2002 ◽  
Vol 107 (3) ◽  
pp. 271-282 ◽  
Author(s):  
Wolfgang Ebeling
Keyword(s):  
Poincaré Series ◽  
Hypersurface Singularity ◽  
Two Dimensional ◽  
Poincare Series

scholarly journals Geometric motivic Poincaré series of quasi-ordinary singularities

2010 ◽  
Vol 149 (1) ◽  
pp. 49-74 ◽  
Author(s):  
HELENA COBO PABLOS ◽  
PEDRO D. GONZÁLEZ PÉREZ
Keyword(s):  
Algebraic Variety ◽  
Poincaré Series ◽  
Explicit Description ◽  
Hypersurface Singularity ◽  
Grothendieck Ring ◽  
Rational Form ◽  
Poincare Series ◽  
Newton Polyhedra ◽  
Complex Algebraic Variety

AbstractThegeometric motivic Poincaré seriesof a germ (S, 0) of complex algebraic variety takes into account the classes in the Grothendieck ring of the jets of arcs through (S, 0). Denef and Loeser proved that this series has a rational form. We give an explicit description of this invariant when (S, 0) is an irreducible germ ofquasi-ordinary hypersurface singularityin terms of the Newton polyhedra of thelogarithmic jacobian ideals. These ideals are determined by thecharacteristic monomialsof a quasi-ordinary branch parametrizing (S, 0).

scholarly journals Poincaré series of multiplier ideals in two-dimensional local rings with rational singularities

2017 ◽  
Vol 304 ◽  
pp. 769-792 ◽  
Author(s):  
Maria Alberich-Carramiñana ◽  
Josep Àlvarez Montaner ◽  
Ferran Dachs-Cadefau ◽  
Víctor González-Alonso
Keyword(s):  
Poincaré Series ◽  
Local Rings ◽  
Two Dimensional ◽  
Poincare Series ◽  
Multiplier Ideals ◽  
Rational Singularities

scholarly journals Poincaré series, 3d gravity and averages of rational CFT

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Viraj Meruliya ◽  
Sunil Mukhi ◽  
Palash Singh
Keyword(s):  
Poincaré Series ◽  
Simons Theory ◽  
Partition Functions ◽  
Moody Algebra ◽  
Modular Invariant ◽  
Poincare Series ◽  
Single Genus ◽  
3D Gravity ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We investigate the Poincaré series approach to computing 3d gravity partition functions dual to Rational CFT. For a single genus-1 boundary, we show that for certain infinite sets of levels, the SU(2)k WZW models provide unitary examples for which the Poincaré series is a positive linear combination of two modular-invariant partition functions. This supports the interpretation that the bulk gravity theory (a topological Chern-Simons theory in this case) is dual to an average of distinct CFT’s sharing the same Kac-Moody algebra. We compute the weights of this average for all seed primaries and all relevant values of k. We then study other WZW models, notably SU(N)1 and SU(3)k, and find that each class presents rather different features. Finally we consider multiple genus-1 boundaries, where we find a class of seed functions for the Poincaré sum that reproduces both disconnected and connected contributions — the latter corresponding to analogues of 3-manifold “wormholes” — such that the expected average is correctly reproduced.

Sign in / Sign up

Export Citation Format

Share Document