For any linear algebraic group G, we define a ring CHBG, the ring of characteristic classes with values in the Chow ring (that is, the ring of algebraic cycles modulo rational equivalence) for… (More)

A fundamental goal of algebraic geometry is to do for singular varieties whatever we can do for smooth ones. Intersection homology, for example, directly produces groups associated to any variety… (More)

Atiyah and Hirzebruch gave the first counterexamples to the Hodge conjecture with integral coefficients [3]. That conjecture predicted that every integral cohomology class of Hodge type (p, p) on a… (More)

The representation theory of the symmetric groups is a classical topic that, since the pioneering work of Frobenius, Schur and Young, has grown into a huge body of theory, with many important… (More)

Preface These are live-texed lecture notes for a course taught in Cambridge during Michaelmas 2013 by Burt Totaro, on a hodgepodge of topics at the intersection of algebraic topology and algebraic… (More)

We prove the equivalence of two fundamental properties of algebraic stacks: being a quotient stack in a strong sense, and the resolution property, which says that every coherent sheaf is a quotient… (More)

The theory of quadratic forms can be regarded as studying an important special case of the general problem of birational classification of algebraic varieties. A typical example of a Fano fibration… (More)

In this paper, inspired by P.M.H. Wilson’s paper on sectional curvatures of Kähler moduli [31], we concentrate on the case where f is a homogeneous polynomial (also called a “form”) of degree d at… (More)

Let K be an algebraically closed field, X a K-scheme, and X(K) the set of closed points in X. A constructible set C ⊆ X(K) is a finite union of subsets Y (K) for finite type K-subschemes Y in X. A… (More)

A closed manifold is called a biquotient if it is diffeomorphic to K\G/H for some compact Lie group G with closed subgroups K and H such that K acts freely on G/H. Every biquotient has a Riemannian… (More)