Flops, flips and perverse point sheaves on threefold stacks

Perverse Sheaves on Image Multiple Point Spaces

Using multiple point spaces some new examples of perverse sheaves on images of maps are described. Furthermore, suppose f : X ! Y is a nite and proper map of complex analytic manifolds of dimension n and n + 1 such that every multiple point space is non-singular and has the dimension expected of a generic map. Then we can describe the composition series for the constant sheaf on the image in th...

Perverse Sheaves on Grassmannians

We give a complete quiver description of the category of perverse sheaves on Hermitian symmetric spaces in types A and D, constructible with respect to the Schubert stratification. The calculation is microlocal, and uses the action of the Borel group to study the geometry of the conormal variety Λ.

Threefold Flops via Matrixfactorization

The explicit McKay correspondence, as formulated by GonzalezSprinberg and Verdier, associates to each exceptional divisor in the minimal resolution of a rational double point, a matrix factorization of the equation of the rational double point. We study deformations of these matrix factorizations, and show that they exist over an appropriate “partially resolved” deformation space for rational d...

Sheaves on Artin Stacks

We develop a theory of quasi–coherent and constructible sheaves on algebraic stacks correcting a mistake in the recent book of Laumon and Moret-Bailly. We study basic cohomological properties of such sheaves, and prove stack–theoretic versions of Grothendieck’s Fundamental Theorem for proper morphisms, Grothendieck’s Existence Theorem, Zariski’s Connectedness Theorem, as well as finiteness Theo...

Sheaves on Algebraic Stacks