On fano 3-folds with non-rational singularities and two-dimensional base

1994 ◽  
Vol 64 (1) ◽  
pp. 249-277 ◽  
Author(s):  
S. Ishii
Keyword(s):  
Two Dimensional ◽  
Rational Singularities

scholarly journals Constancy regions of mixed multiplier ideals in two-dimensional local rings with rational singularities

2017 ◽  
Vol 291 (2-3) ◽  
pp. 245-263 ◽  
Author(s):  
Maria Alberich-Carramiñana ◽  
Josep Àlvarez Montaner ◽  
Ferran Dachs-Cadefau
Keyword(s):  
Local Rings ◽  
Two Dimensional ◽  
Multiplier Ideals ◽  
Rational Singularities

scholarly journals A characterization of two-dimensional rational singularities via core of ideals

2018 ◽  
Vol 499 ◽  
pp. 450-468 ◽  
Author(s):  
Tomohiro Okuma ◽  
Kei-ichi Watanabe ◽  
Ken-ichi Yoshida
Keyword(s):  
Two Dimensional ◽  
Rational Singularities

On Adjacent Ideals in Two-Dimensional Rational Singularities

2009 ◽  
Vol 38 (1) ◽  
pp. 308-331 ◽  
Author(s):  
R. Debremaeker ◽  
V. Van Lierde
Keyword(s):  
Two Dimensional ◽  
Rational Singularities

ALMOST ADJACENT IDEALS IN TWO-DIMENSIONAL MUHLY RATIONAL SINGULARITIES

2013 ◽  
Vol 13 (03) ◽  
pp. 1350115
Author(s):  
V. VAN LIERDE
Keyword(s):  
Residue Field ◽  
Closed Domain ◽  
Rational Singularity ◽  
Two Dimensional ◽  
Associated Graded Ring ◽  
Graded Ring ◽  
Rational Singularities ◽  
Integrally Closed

Let (R, m) be a two-dimensional Muhly rational singularity, i.e. the residue field R/m is algebraically closed and the associated graded ring is an integrally closed domain. The goal of this paper is to use immediate quadratic transforms and degree coefficients to investigate complete ideals that are almost adjacent to m, i.e. [Formula: see text].

scholarly journals ULRICH IDEALS AND MODULES OVER TWO-DIMENSIONAL RATIONAL SINGULARITIES

2016 ◽  
Vol 221 (1) ◽  
pp. 69-110 ◽  
Author(s):  
SHIRO GOTO ◽  
KAZUHO OZEKI ◽  
RYO TAKAHASHI ◽  
KEI-ICHI WATANABE ◽  
KEN-ICHI YOSHIDA
Keyword(s):  
Point Of View ◽  
Two Dimensional ◽  
Double Points ◽  
Rational Singularities ◽  
Geometric Point ◽  
The Relationship

The main aim of this paper is to classify Ulrich ideals and Ulrich modules over two-dimensional Gorenstein rational singularities (rational double points) from a geometric point of view. To achieve this purpose, we introduce the notion of (weakly) special Cohen–Macaulay modules with respect to ideals, and study the relationship between those modules and Ulrich modules with respect to good ideals.

scholarly journals Multiplier ideals in two-dimensional local rings with rational singularities

2016 ◽  
Vol 65 (2) ◽  
pp. 287-320 ◽  
Author(s):  
Maria Alberich-Carramiñana ◽  
Josep Àlvarez Montaner ◽  
Ferran Dachs-Cadefau
Keyword(s):  
Local Rings ◽  
Two Dimensional ◽  
Multiplier Ideals ◽  
Rational Singularities

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

CONNECTING RANDOM MATRIX AND TOPOLOGICAL LG MODELS VIA INTEGRABILITY

1991 ◽  
Vol 06 (31) ◽  
pp. 2837-2842
Author(s):  
K. HERZIG ◽  
M. WEISSGOLD ◽  
P. TATARU-MIHA
Keyword(s):  
Hamiltonian System ◽  
Characteristic Polynomial ◽  
Double Point ◽  
Jacobi Matrix ◽  
String Equation ◽  
Two Dimensional ◽  
Point Singularity ◽  
Rational Double Point ◽  
Rational Singularities ◽  
Double Eigenvalue

We prove that a bi-Hamiltonian system (e.g., a KdV system) is integrable if and only if its Krichever–Moser–Jacobi matrix L has a double eigenvalue, i.e., if (the characteristic polynomial of) L has rational double point singularities. Therefore, L (precisely, its characteristic polynomial) can be identified with the potential of a Landau–Ginzburg (LG) topological model with the same (rational double point) singularity. A rational curve is naturally defined in the corresponding Kummer variety and this explains the appearance (or non-appearance) of the doubling of the string equation as well as a phenomenon observed by Eguchi et al. Finally, we point out a parallelism between rational two-dimensional theories and rational singularities.

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