arXiv subjects
Publications and source records attributed to Edward Dewey.
Given a very general abelian fivefold $A$ and a principal polarization $Θ\subset A$, we construct surfaces generating the algebraic part of the middle cohomology $H^4(Θ, {\mathbb Q})$, and determine the intersection pairing between these surfaces. In particular, we obtain a new proof of the Hodge conjecture for $H^4(Θ, {\mathbb Q})$ and show that it contains a copy of the root lattice of $E_6$.
We study the stack M of cameral covers for a complex reductive group G, introduced by Donagi and Gaitsgory. We compute its rational cohomology ring. In the special case G=GL(n), M is the stack of spectral covers. We also compute the cohomology ring of the stack of abstract regular G-Higgs bundles.
Let $G$ be a connected affine algebraic group over $\mathbb{C}$, $G \to X$ be an open immersion of $G$-varieties, $Z = X-G$ and $i: Z \to X$ be the inclusion. Let $α\in H^*(G,\mathbb{C})$ be primitive. We give a method to compute the image of $α$ in $H^*(Z, i^!\mathbb{C}_X)$, using a lift of $α$ along the first edge map of the Čech spectral sequence for $H^*(BG, \mathbb{C})$. We apply it to the wonderful compactification of a centerless semisimple group $G$.