Toric Manifolds

2004 ◽  
pp. 225-270
Author(s):  
Michèle Audin
Keyword(s):  
Toric Manifolds

scholarly journals Gauge theories on compact toric manifolds

2021 ◽  
Vol 111 (3) ◽  
Author(s):  
Giulio Bonelli ◽  
Francesco Fucito ◽  
Jose Francisco Morales ◽  
Massimiliano Ronzani ◽  
Ekaterina Sysoeva ◽  
...  
Keyword(s):  
Partition Function ◽  
Gauge Theories ◽  
Blow Up ◽  
Gauge Coupling ◽  
Piecewise Constant Function ◽  
Partition Functions ◽  
Piecewise Constant ◽  
Toric Manifolds ◽  
Holomorphic Anomaly ◽  
The One

AbstractWe compute the $$\mathcal{N}=2$$ N = 2 supersymmetric partition function of a gauge theory on a four-dimensional compact toric manifold via equivariant localization. The result is given by a piecewise constant function of the Kähler form with jumps along the walls where the gauge symmetry gets enhanced. The partition function on such manifolds is written as a sum over the residues of a product of partition functions on $$\mathbb {C}^2$$ C 2 . The evaluation of these residues is greatly simplified by using an “abstruse duality” that relates the residues at the poles of the one-loop and instanton parts of the $$\mathbb {C}^2$$ C 2 partition function. As particular cases, our formulae compute the SU(2) and SU(3) equivariant Donaldson invariants of $$\mathbb {P}^2$$ P 2 and $$\mathbb {F}_n$$ F n and in the non-equivariant limit reproduce the results obtained via wall-crossing and blow up methods in the SU(2) case. Finally, we show that the U(1) self-dual connections induce an anomalous dependence on the gauge coupling, which turns out to satisfy a $$\mathcal {N}=2$$ N = 2 analog of the $$\mathcal {N}=4$$ N = 4 holomorphic anomaly equations.

scholarly journals Toric extremal Kähler-Ricci solitons are Kähler-Einstein

2017 ◽  
Vol 4 (1) ◽  
pp. 179-182 ◽  
Author(s):  
Simone Calamai ◽  
David Petrecca
Keyword(s):  
General Problem ◽  
Short Note ◽  
Kähler Manifold ◽  
Ricci Soliton ◽  
Ricci Solitons ◽  
Toric Manifolds ◽  
Kahler Manifold

Abstract In this short note, we prove that a Calabi extremal Kähler-Ricci soliton on a compact toric Kähler manifold is Einstein. This settles for the class of toric manifolds a general problem stated by the authors that they solved only under some curvature assumptions.

scholarly journals Quaternionic toric manifolds

2019 ◽  
Vol 17 (1) ◽  
pp. 267-300 ◽  
Author(s):  
Graziano Gentili ◽  
Anna Gori ◽  
Giulia Sarfatti
Keyword(s):  
Toric Manifolds

scholarly journals Symplectic Capacities of Toric Manifolds and Related Results

2006 ◽  
Vol 181 ◽  
pp. 149-184 ◽  
Author(s):  
Guangcun Lu
Keyword(s):  
Line Bundle ◽  
Blow Up ◽  
Ample Line Bundle ◽  
Symplectic Manifolds ◽  
Toric Manifolds ◽  
Seshadri Constant ◽  
Combinatorial Data

AbstractIn this paper we give concrete estimations for the pseudo symplectic capacities of toric manifolds in combinatorial data. Some examples are given to show that our estimates can compute their pseudo symplectic capacities. As applications we also estimate the symplectic capacities of the polygon spaces. Other related results are impacts of symplectic blow-up on symplectic capacities, symplectic packings in symplectic toric manifolds, the Seshadri constant of an ample line bundle on toric manifolds, and symplectic capacities of symplectic manifolds withS1-action.

scholarly journals Nonrational symplectic toric cuts

2018 ◽  
Vol 29 (10) ◽  
pp. 1850063 ◽  
Author(s):  
Fiammetta Battaglia ◽  
Elisa Prato
Keyword(s):  
Toric Manifolds ◽  
Blowing Up

In this paper, we extend cutting and blowing up to the nonrational symplectic toric setting. This entails the possibility of cutting and blowing up for symplectic toric manifolds and orbifolds in nonrational directions.

Embedding theorems for quasi-toric manifolds given by combinatorial data

2015 ◽  
Vol 79 (6) ◽  
pp. 1157-1183
Author(s):  
V M Buchstaber ◽  
A A Kustarev
Keyword(s):  
Embedding Theorems ◽  
Toric Manifolds ◽  
Combinatorial Data

scholarly journals Remarks on Lagrangian intersections in toric manifolds

2012 ◽  
Vol 365 (7) ◽  
pp. 3851-3875 ◽  
Author(s):  
Miguel Abreu ◽  
Leonardo Macarini
Keyword(s):  
Toric Manifolds
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