Canadian Mathematical Society
Canadian Mathematical Society
  location:  Publicationsjournals
Search results

Search: All articles in the CJM digital archive with keyword Weyl group

  Expand all        Collapse all Results 1 - 2 of 2

1. CJM Online first

Ehrig, Michael; Stroppel, Catharina
2-row Springer fibres and Khovanov diagram algebras for type D
We study in detail two row Springer fibres of even orthogonal type from an algebraic as well as topological point of view. We show that the irreducible components and their pairwise intersections are iterated $\mathbb{P}^1$-bundles. Using results of Kumar and Procesi we compute the cohomology ring with its action of the Weyl group. The main tool is a type $\operatorname D$ diagram calculus labelling the irreducible components in a convenient way which relates to a diagrammatical algebra describing the category of perverse sheaves on isotropic Grassmannians based on work of Braden. The diagram calculus generalizes Khovanov's arc algebra to the type $\operatorname D$ setting and should be seen as setting the framework for generalizing well-known connections of these algebras in type $\operatorname A$ to other types.

Keywords:Springer fibers, Khovanov homology, Weyl group type D

2. CJM 2000 (vol 52 pp. 123)

Harbourne, Brian
An Algorithm for Fat Points on $\mathbf{P}^2
Let $F$ be a divisor on the blow-up $X$ of $\pr^2$ at $r$ general points $p_1, \dots, p_r$ and let $L$ be the total transform of a line on $\pr^2$. An approach is presented for reducing the computation of the dimension of the cokernel of the natural map $\mu_F \colon \Gamma \bigl( \CO_X(F) \bigr) \otimes \Gamma \bigl( \CO_X(L) \bigr) \to \Gamma \bigl( \CO_X(F) \otimes \CO_X(L) \bigr)$ to the case that $F$ is ample. As an application, a formula for the dimension of the cokernel of $\mu_F$ is obtained when $r = 7$, completely solving the problem of determining the modules in minimal free resolutions of fat point subschemes\break $m_1 p_1 + \cdots + m_7 p_7 \subset \pr^2$. All results hold for an arbitrary algebraically closed ground field~$k$.

Keywords:Generators, syzygies, resolution, fat points, maximal rank, plane, Weyl group
Categories:13P10, 14C99, 13D02, 13H15

© Canadian Mathematical Society, 2015 :