On Landsberg's criterion for complete intersections.
On linked surfaces in .
On Manifolds Locally Modelled on Non-Riemannian Homogeneous Spaces.
On Monomial curves and Cohen-Macaulay type.
On Monomial k-Buchsbaum curves in P3.
On multiplicities of points on Schubert varieties in Grassmannians.
On multivariate Descartes' rule – a counterexample.
On orbits of the automorphism group on an affine toric variety
Let X be an affine toric variety. The total coordinates on X provide a canonical presentation of X as a quotient of a vector space by a linear action of a quasitorus. We prove that the orbits of the connected component of the automorphism group Aut(X) on X coincide with the Luna strata defined by the canonical quotient presentation.
On parabolic Whittaker functions II
We propose a Givental-type stationary phase integral representation for the restricted Grm,N-Whittaker function, which is expected to describe the (S 1×U N)-equivariant Gromov-Witten invariants of the Grassmann variety Grm,N. Our key tool is a generalization of the Whittaker model for principal series U(gl N)-modules, and its realization in the space of functions of totally positive unipotent matrices. In particular, our construction involves a representation theoretic derivation of the Batyrev-Ciocan-Fontanine-Kim-van...
On Plurigenera of Normal Isolated Singularities. I.
On projective equivalence of univariate polynomial subspaces.
On Projective Resolutions of Frobenius Algebras and Gorenstein Rings.
On projective toric varieties whose defining ideals have minimal generators of the highest degree
It is known that generators of ideals defining projective toric varieties of dimension embedded by global sections of normally generated line bundles have degree at most . We characterize projective toric varieties of dimension whose defining ideals must have elements of degree as generators.
On Projective Varieties of Codimension 2.
On quasihomogeneous manifolds – via Brion-Luna-Vust theorem
We consider a smooth projective variety on which a simple algebraic group acts with an open orbit. We discuss a theorem of Brion-Luna-Vust in order to relate the action of with the induced action of on the normal bundle of a closed orbit of the action. We get effective results in case and .
On radical-equivalent and zero-equivalent ideals
On Rao's theorems and the Lazarsfeld-Rao property
On real flag manifolds with cup-length equal to its dimension
We prove that for any positive integers there exists a real flag manifold with cup-length equal to its dimension. Additionally, we give a necessary condition that an arbitrary real flag manifold needs to satisfy in order to have cup-length equal to its dimension.
On representations of with algebras of invariants being complete intersections.
On Schubert Varieties in the Flag Manifold of SI (n, C).