scholarly journals Intersection cohomology and quantum cohomology of conical symplectic resolutions

2015 ◽  
Vol 2 (5) ◽  
pp. 623-641 ◽  
Author(s):  
Michael McBreen ◽  
Nicholas Proudfoot
Keyword(s):  
Quantum Cohomology ◽  
Intersection Cohomology ◽  
Symplectic Resolutions

scholarly journals Polynomial identities related to special Schubert varieties

2021 ◽  
Author(s):  
Francesca Cioffi ◽  
Davide Franco ◽  
Carmine Sessa
Keyword(s):  
Arbitrary Number ◽  
Schubert Variety ◽  
Decomposition Theorem ◽  
Point Of View ◽  
Explicit Description ◽  
Intersection Cohomology ◽  
Schubert Varieties ◽  
Polynomial Identities ◽  
Poincaré Polynomial

AbstractLet $$\mathcal S$$ S be a single condition Schubert variety with an arbitrary number of strata. Recently, an explicit description of the summands involved in the decomposition theorem applied to such a variety has been obtained in a paper of the second author. Starting from this result, we provide an explicit description of the Poincaré polynomial of the intersection cohomology of $$\mathcal S$$ S by means of the Poincaré polynomials of its strata, obtaining interesting polynomial identities relating Poincaré polynomials of several Grassmannians, both by a local and by a global point of view. We also present a symbolic study of a particular case of these identities.

scholarly journals Wilson loop algebras and quantum K-theory for Grassmannians

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Hans Jockers ◽  
Peter Mayr ◽  
Urmi Ninad ◽  
Alexander Tabler
Keyword(s):  
Wilson Loop ◽  
Gauge Theories ◽  
Wilson Line ◽  
Quantum Cohomology ◽  
Three Dimensional ◽  
Loop Algebra ◽  
Loop Algebras ◽  
Verlinde Algebra ◽  
K Theory ◽  
Chern Simons

Abstract We study the algebra of Wilson line operators in three-dimensional $$ \mathcal{N} $$ N = 2 supersymmetric U(M ) gauge theories with a Higgs phase related to a complex Grassmannian Gr(M, N ), and its connection to K-theoretic Gromov-Witten invariants for Gr(M, N ). For different Chern-Simons levels, the Wilson loop algebra realizes either the quantum cohomology of Gr(M, N ), isomorphic to the Verlinde algebra for U(M ), or the quantum K-theoretic ring of Schubert structure sheaves studied by mathematicians, or closely related algebras.

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 COMPLETION OF THE CONJECTURE: QUANTUM COHOMOLOGY OF FANO HYPERSURFACES

2000 ◽  
Vol 15 (02) ◽  
pp. 101-120 ◽  
Author(s):  
MASAO JINZENJI
Keyword(s):  
Quantum Cohomology

In this letter, we propose the formulas that compute all the rational structural constants of the quantum Kähler subring of Fano hypersurfaces.

scholarly journals Donaldson–Thomas invariants versus intersection cohomology of quiver moduli

2019 ◽  
Vol 2019 (754) ◽  
pp. 143-178 ◽  
Author(s):  
Sven Meinhardt ◽  
Markus Reineke
Keyword(s):  
Moduli Space ◽  
Stability Condition ◽  
Intersection Cohomology ◽  
Quiver Representations ◽  
Compactly Supported ◽  
Generic Stability ◽  
Relative Version ◽  
Zero Potential ◽  
Stable Locus

Abstract The main result of this paper is the statement that the Hodge theoretic Donaldson–Thomas invariant for a quiver with zero potential and a generic stability condition agrees with the compactly supported intersection cohomology of the closure of the stable locus inside the associated coarse moduli space of semistable quiver representations. In fact, we prove an even stronger result relating the Donaldson–Thomas “function” to the intersection complex. The proof of our main result relies on a relative version of the integrality conjecture in Donaldson–Thomas theory. This will be the topic of the second part of the paper, where the relative integrality conjecture will be proven in the motivic context.

scholarly journals Intersection cohomology of moduli spaces of sheaves on surfaces

2018 ◽  
Vol 24 (5) ◽  
pp. 3889-3926 ◽  
Author(s):  
Jan Manschot ◽  
Sergey Mozgovoy
Keyword(s):  
Moduli Spaces ◽  
Intersection Cohomology ◽  
Moduli Spaces Of Sheaves
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