Minimal rational curves on wonderful group compactifications

Standard monomials for wonderful group compactifications

Let X be the wonderful compactification of the semisimple adjoint algebraic group G. We show that the basis of H0(X,L) constructed in [CM03] is compatible with all B×B-orbit closures in X by defining subsets using only combinatorics of the underlying paths. Furthermore, we construct standard monomials on X that have properties similar to classical standard monomials.

Remarks on Lines and Minimal Rational Curves

We determine all of lines in the moduli space M of stable bundles for arbitrary rank and degree. A further application of minimal rational curves is also given in last section.

Wonderful Compactifications of Arrangements of Subvarieties

We define the wonderful compactification of an arrangement of subvarieties. Given a complex nonsingular algebraic variety Y and certain collection G of subvarieties of Y , the wonderful compactification YG can be constructed by a sequence of blow-ups of Y along the subvarieties of the arrangement. This generalizes the Fulton-MacPherson configuration spaces and the wonderful models given by De C...

Chow Motive of Fulton-macpherson Configuration Spaces and Wonderful Compactifications

The purpose of this article is to study the Chow groups and Chow motives of the so-called wonderful compactifications of an arrangement of subvarieties, in particular the Fulton-MacPherson configuration spaces. All the varieties in the paper are over an algebraically closed field. Let Y be a nonsingular quasi-projective variety. Let S be an arrangement of subvarieties of Y (cf. Definition 2.2)....

Rational Curves on Varieties