相关论文: Nilpotent slices, Hilbert schemes, and the Jones p…

In an earlier paper, we introduced a knot invariant for a null-homologous knot K in an oriented three-manifold Y, which is closely related to the Heegaard Floer homology of Y. In this paper we investigate some properties of these knot…

We undertake a detailed study of the geometry of Bottacin's Poisson structures on Hilbert schemes of points in Poisson surfaces, i.e. smooth complex surfaces equipped with an effective anticanonical divisor. We focus on three themes that,…

By proving a connected sum formula for the Legendrian invariant $\lambda_+$ in knot Floer homology we exhibit infinitely many transversely non simple knots.

We define an algebraic/combinatorial object on the front projection $\Sigma$ of a Legendrian knot called a Morse complex sequence, abbreviated MCS. This object is motivated by the theory of generating families and provides new connections…

Starting from a general $\mathcal{N} = 2$ SCFT, we study the network of $\mathcal{N} = 1$ SCFTs obtained from relevant deformations by nilpotent mass parameters. We also study the case of flipper field deformations where the mass parameters…

In this paper, we focus on the variety $\mathbf{NF}_3$ generated by all flat semirings with $3$-nilpotent multiplicative reducts. By introducing graph semirings, we characterize all subdirectly irreducible members of $\mathbf{NF}_3$. We…

Given a semisimple element in the loop Lie algebra of a reductive group, we construct a quasi-coherent sheaf on a partial resolution of the trigonometric commuting variety of the Langlands dual group. The construction uses affine Springer…

Let $G$ be a split semisimple linear algebraic group over a field and let $X$ be a generic twisted flag variety of $G$. Extending the Hilbert basis techniques to Laurent polynomials over integers we give an explicit presentation of the…

There have been a number of constructions of Lagrangian Floer homology invariants for $3$-manifolds defined in terms of symplectic character varieties arising from Heegaard splittings. With the aim of establishing an Atiyah-Floer…

We generalise statements known about Springer fibres associated to nilpotents with 2 Jordan blocks to Spaltenstein varieties. We study the geometry of generalised irreducible components (i.e. Bialynicki-Birula cells) and their pairwise…

We give some examples of non-complete invariant affine connections on nilpotent and filiform Lie groups. This permits to describe non-nilpotent faithful representations on the model of filiform n-dimensional Lie algebras and, in particular,…

We realise Stroppel's extended arc algebra in the Fukaya-Seidel category of a natural Lefschetz fibration on the generic fiber of the adjoint quotient map on a type $A$ nilpotent slice with two Jordan blocks, and hence obtain a symplectic…

The intersection of a complex plane curve with a small three-sphere surrounding one of its singularities is a non-trivial link. The refined punctual Hilbert schemes of the singularity parameterize subschemes supported at the singular point…

Let $K$ be an algebraically closed field with characteristic zero, and $\mathfrak{g}$ a Lie algebra. Let $Y(\mathfrak{g})$ be the subalgebra of the symmetric algebra $S(\mathfrak{g})=K[\mathfrak{g}^*]$ made of the polynomials which are…

We construct families of functions in involution for transverse Poisson structures at nilpotent elements of Lie-Poisson structures on simple Lie algebras by using the argument shift method. Examples show that these families contain…

We give an example of a 3-component smoothly slice boundary link, each of whose components has a genus one Seifert surface, such that any metaboliser of the boundary link Seifert form is represented by 3 curves on the Seifert surfaces that…

We construct a categorification of the maximal commutative subalgebra of the type $A$ Hecke algebra. Specifically, we propose a monoidal functor from the (symmetric) monoidal category of coherent sheaves on the flag Hilbert scheme to the…

We compare two different types of mapping class invariants: the Hochschild homology of an $A_\infty$ bimodule coming from bordered Heegaard Floer homology, and fixed point Floer cohomology. We first compute the bimodule invariants and their…

Various algebraic structures have recently appeared in a parallel way in the framework of Hilbert schemes of points on a surface and respectively in the framework of equivariant K-theory [N1,Gr,S2,W], but direct connections are yet to be…

Let $G$ be a connected reductive group over an algebraically closed field $k$, and let $Fl$ be the affine flag variety of $G$. For every regular semisimple element $\gamma$ of $G(k((t)))$, the affine Springer fiber $Fl_{\gamma}$ can be…