Rational homogeneous spaces as geometric realizations of birational transformations

A Geometric View of Rational Landen Transformations

In this paper, a geometric interpretation is provided of a new rational Landen transformation. The convergence of its iterates is also established.

HyperKähler Manifolds and Birational Transformations

The minimal model program has greatly enhanced our knowledge on birational geometry of varieties of dimension 3 and higher. About the same time, the last two decades have also witnessed increasing interests in HyperKähler manifolds, a particular class of Calabi-Yau manifolds. One interest in this area, which we hope to treat in the future, is to investigate the behavior of the SYZ mirror conjec...

Quantum Homogeneous Spaces as Quantum Quotient Spaces

We show that certain embeddable homogeneous spaces of a quantum group that do not correspond to a quantum subgroup still have the structure of quantum quotient spaces. We propose a construction of quantum fibre bundles on such spaces. The quantum plane and the general quantum two-spheres are discussed in detail. 0. Introduction A homogeneous space X of a Lie group G may be always identified wit...

Birational Geometry of the Space of Rational Curves in Homogeneous Varieties

In this thesis, we investigate the birational geometry of the space of rational curves in various homogeneous spaces, with a focus on the quasi-map compactification induced by the Quot and Hyperquot functors. We first study the birational geometry of the Quot scheme of sheaves on P1 via techniques from the Mori program, explicitly describing its associated cones of ample and effective divisors ...

Geometric Realizations of Substitutions