Related papers: 2-block Springer fibers: convolution algebras and …

This paper gives insight into intriguing connections between two apparently unrelated theories: the theory of skein modules of 3-manifolds and the theory of representations of groups into special linear groups of 2 by 2 matrices. Let R be a…

Monoidal product, braiding, balancing and weak duality are pieces of algebraic information that are well-known to have their origin in oriented genus zero surfaces and their mapping classes. More precisely, each of them correspond to…

The Gieseker-Uhlenbeck morphism maps the Gieseker moduli space of stable rank-2 sheaves on a smooth projective surface to the Uhlenbeck compactification, and is a generalization of the Hilbert-Chow morphism for Hilbert schemes of points.…

We determine the structure of the BPS algebra of 2-Calabi-Yau Abelian categories for which the stack of objects admits a good moduli space. We prove that this algebra is isomorphic to the positive part of the enveloping algebra of a…

For $n \geq 1$, the twistor space $\mathfrak{Z}(\mathbb{S}^{2n})$ of the conformal $2n$-sphere is biholomorphic to the Zariski closure, taken in the complex Grassmannian manifold $\mathbf{G}(n+1, 2n+2)$, of the set of graphs of…

Since the appearance of the paper by Bilal & al. in 1991, it has been widely assumed that W-algebras originating from the Hamiltonian reduction of an SL(n,C)-bundle over a Riemann surface give rise to a flat connection, in which the…

We introduce a dynamical Mordell-Lang-type conjecture for coherent sheaves. When the sheaves are structure sheaves of closed subschemes, our conjecture becomes a statement about unlikely intersections. We prove an analogue of this…

We study birational maps among 1) the moduli space of semistable torsion sheaves of Hilbert polynomial $4m+2$ on a smooth quadric surface, 2) the moduli space of semistable torsion sheaves of Hilbert polynomial $m^{2}+3m+2$ on…

We compute the coherent cohomology of the structure sheaf of complex periplectic Grassmannians. In particular, we show that it can be decomposed as a tensor product of the singular cohomology ring of a Grassmannian for either the symplectic…

We identify Le Potier's moduli spaces of limit stable pairs $(F,s)$, where $F$ is a 2-dimensional sheaf on a nonsingular projective 4-fold $X$ and $s \in H^0(F)$, with the moduli spaces of polynomial stable 2-term complexes in derived…

As already observed by Gabriel, coherent sheaves on schemes obtained by gluing affine open subsets can be described by a simple gluing construction. An example due to Ferrand shows that this fails in general for pushouts along closed…

The Springer correspondence makes a link between the characters of a Weyl group and the geometry of the nilpotent cone of the corresponding semisimple Lie algebra. In this article, we consider a modular version of the theory, and show that…

We study the differential and Riemannian geometry of algebras $A$ endowed with an action of a triangular Hopf algebra $H$ and noncommutativity compatible with the associated braiding. The modules of one forms and of braided derivations are…

We study the behavior of blocks in flat families of finite-dimensional algebras. In a general setting we construct a finite directed graph encoding a stratification of the base scheme according to the block structures of the fibers. This…

We prove similar theorems concerning the structure of bundles involving complements of fiber-type hyperplane arrangements and orbit configuration spaces. These results facilitate analysis of the fundamental groups of these spaces, which may…

We decompose the fibers of the Springer resolution for the odd nilcone of the Lie superalgebra $\osp(2n+1,2n)$ into locally closed subsets. We use this decomposition to prove that almost all fibers are connected. However, in contrast with…

A criterion for a functor between derived categories of coherent sheaves to be full and faithful is given. A semiorthogonal decomposition for the derived category of coherent sheaves on the intersection of two even dimensional quadrics is…

We give a geometric interpretation of the Jones-Ocneanu trace on the Hecke algebra, using the equivariant cohomology of sheaves on SL(n). This construction makes sense for all simple algebraic groups, so we obtain a generalization of the…

According to Laumon, an affine Springer fiber is homeomorphic to the universal abelian covering of the compactified Jacobian of a spectral curve. We construct equivariant deformations $f_{n}:\overline{\mathcal{P}}_{n}\to \mathcal{B}_{n}$ of…

Let $M= G/\Gamma$ be a compact nilmanifold endowed with an invariant complex structure. We prove that, on an open set of any connected component of the moduli space ${\cal C} ({\frak g})$ of invariant complex structures on $M$, the…