That this is feasible is supported by three recent articles of the applicant and the host where combining their techniques led to the solution of a long-awaited results on the dimension of certain

algebraic varieties appearing in the context of quantum algebras.

Bott-Samelson varieties are smooth, irreducible and [absolute value of Q]-dimensional

algebraic varieties.

Topology of

algebraic varieties and singularities; proceedings.

The main focus is rational points on

algebraic varieties over non-algebraically closed fields.

These are so-called

algebraic varieties, which are the zero-sets of polynomials, and certain geometric objects called manifolds," he added.

The label "quantized coordinate ring" is used in the literature to refer to various non-communicative algebras which are, informally expressed, deformations of the classical coordinate rings of

algebraic varieties or algebraic groups; the adjective "quantized" usually indicates that some solution to the quantum Yang-Baxter equation is involved in the construction and/or the representation theory of the algebra.

The 16 papers report some of the many radical developments in the quest to understand the structure of

algebraic varieties since 2005.

Brion, Lectures on the geometry of flag varieties, in Topics in cohomological studies of

algebraic varieties, Trends Math.

Residues and duality for projective

algebraic varieties.

Arc spaces have first appeared in the work of John Nash (see Nash (1995)) to study resolution of singularities of

algebraic varieties.

In addition to original articles, the book contains three surveys devoted to singularities of theta divisors, compactified Jacobians of singular curves, and 'strange duality' among moduli spaces of vector bundles on

algebraic varieties.

Some subjects examined include purely inseparable k-forms of affine algebraic curves, bad field generators, coordinates in ideals of polynomial algebras, and equivariant cancellation for

algebraic varieties.