scholarly journals On the (non)existence of symplectic resolutions of linear quotients

2016 ◽  
Vol 23 (6) ◽  
pp. 1537-1564 ◽  
Author(s):  
Gwyn Bellamy ◽  
Travis Schedler
Keyword(s):  
Symplectic Resolutions ◽  
Linear Quotients

scholarly journals WREATH PRODUCTS, NILPOTENT ORBITS AND SYMPLECTIC DEFORMATIONS

2007 ◽  
Vol 18 (05) ◽  
pp. 473-481
Author(s):  
BAOHUA FU
Keyword(s):  
Wreath Product ◽  
Wreath Products ◽  
Nilpotent Orbit ◽  
Nilpotent Orbits ◽  
Symplectic Resolutions

We recover the wreath product X ≔ Sym 2(ℂ2/± 1) as a transversal slice to a nilpotent orbit in 𝔰𝔭6. By using deformations of Springer resolutions, we construct a symplectic deformation of symplectic resolutions of X.

scholarly journals A software package for Mori dream spaces

2015 ◽  
Vol 18 (1) ◽  
pp. 647-659 ◽  
Author(s):  
Jürgen Hausen ◽  
Simon Keicher
Keyword(s):  
Software Package ◽  
Toric Varieties ◽  
Quotient Singularity ◽  
Algebraic Varieties ◽  
Cox Rings ◽  
Cox Ring ◽  
Mori Dream Spaces ◽  
The Common ◽  
Symplectic Resolutions

Mori dream spaces form a large example class of algebraic varieties, comprising the well-known toric varieties. We provide a first software package for the explicit treatment of Mori dream spaces and demonstrate its use by presenting basic sample computations. The software package is accompanied by a Cox ring database which delivers defining data for Cox rings and Mori dream spaces in a suitable format. As an application of the package, we determine the common Cox ring for the symplectic resolutions of a certain quotient singularity investigated by Bellamy–Schedler and Donten-Bury–Wiśniewski.

Linear quotients of Artinian Weak Lefschetz algebras

2013 ◽  
Vol 217 (10) ◽  
pp. 1955-1966 ◽  
Author(s):  
Giuseppe Favacchio ◽  
Alfio Ragusa ◽  
Giuseppe Zappalà
Keyword(s):  
Linear Quotients

scholarly journals Betti numbers of toric ideals of graphs: A case study

2019 ◽  
Vol 18 (12) ◽  
pp. 1950226
Author(s):  
Federico Galetto ◽  
Johannes Hofscheier ◽  
Graham Keiper ◽  
Craig Kohne ◽  
Adam Van Tuyl ◽  
...  
Keyword(s):  
Bipartite Graph ◽  
Hilbert Series ◽  
Complete Bipartite Graph ◽  
Betti Numbers ◽  
Toric Ideals ◽  
Toric Ideal ◽  
Initial Ideal ◽  
Graded Betti Numbers ◽  
Linear Quotients

We compute the graded Betti numbers for the toric ideal of a family of graphs constructed by adjoining a cycle to a complete bipartite graph. The key observation is that this family admits an initial ideal which has linear quotients. As a corollary, we compute the Hilbert series and [Formula: see text]-vector for all the toric ideals of graphs in this family.

k-Decomposable Monomial Ideals

2015 ◽  
Vol 22 (spec01) ◽  
pp. 745-756 ◽  
Author(s):  
Rahim Rahmati-Asghar ◽  
Siamak Yassemi
Keyword(s):  
Simplicial Complex ◽  
Monomial Ideals ◽  
Alexander Dual ◽  
Linear Quotients ◽  
Dimensional Simplicial Complex

In this paper we introduce a class of monomial ideals, called k-decomposable ideals. It is shown that the class of k-decomposable ideals is contained in the class of monomial ideals with linear quotients, and when k is large enough, the class of k-decomposable ideals is equal to the class of ideals with linear quotients. In addition, it is shown that a d-dimensional simplicial complex is k-decomposable if and only if the Stanley-Reisner ideal of its Alexander dual is a k-decomposable ideal, where k ≤ d. Moreover, it is shown that every k-decomposable ideal is componentwise k-decomposable.

scholarly journals On categories for quantized symplectic resolutions

2017 ◽  
Vol 153 (12) ◽  
pp. 2445-2481 ◽  
Author(s):  
Ivan Losev
Keyword(s):  
Fixed Points ◽  
Hyperplane Arrangement ◽  
Derived Equivalences ◽  
Real Hyperplane ◽  
Symplectic Resolutions

In this paper we study categories ${\mathcal{O}}$ over quantizations of symplectic resolutions admitting Hamiltonian tori actions with finitely many fixed points. In this generality, these categories were introduced by Braden et al. We establish a family of standardly stratified structures (in the sense of the author and Webster) on these categories ${\mathcal{O}}$. We use these structures to study shuffling functors of Braden et al. (called cross-walling functors in this paper). Most importantly, we prove that all cross-walling functors are derived equivalences that define an action of the Deligne groupoid of a suitable real hyperplane arrangement.

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