The Hilbert pairing for formal groups over -rings.
The ideal of relations for the ring of invariants of points on the line
The ring of projective invariants of ordered points on the projective line is one of the most basic and earliest studied examples in Geometric Invariant Theory. It is a remarkable fact and the point of this paper that, unlike its close relative the ring of invariants of unordered points, this ring can be completely and simply described. In 1894 Kempe found generators for this ring, thereby proving the First Main Theorem for it (in the terminology introduced by Weyl). In this paper we compute...
The incidence class and the hierarchy of orbits
R. Rimányi defined the incidence class of two singularities η and ζ as [η]|ζ, the restriction of the Thom polynomial of η to ζ. He conjectured that (under mild conditions) [η]|ζ ≠ 0 ⇔ ζ ⊂ . Generalizing this notion we define the incidence class of two orbits η and ζ of a representation. We give a sufficient condition (positivity) for ζ to have the property that [η]|ζ ≠ 0 ⇔ ζ ⊂ for any other orbit η. We show that for many interesting cases, e.g. the quiver representations of Dynkin type positivity...
The index of centralizers of elements of reductive Lie algebras.
The Invariants of Unipotent Radicals of Parabolic Subgroups.
The Irregularities of Hirzebruch's Examples of Surfaces of General Type with c21= 3c2 .
The jacobian map, the jacobian group and the group of automorphisms of the Grassmann algebra
There are nontrivial dualities and parallels between polynomial algebras and the Grassmann algebras (e.g., the Grassmann algebras are dual of polynomial algebras as quadratic algebras). This paper is an attempt to look at the Grassmann algebras at the angle of the Jacobian conjecture for polynomial algebras (which is the question/conjecture about the Jacobian set– the set of all algebra endomorphisms of a polynomial algebra with the Jacobian – the Jacobian conjecture claims that the Jacobian...
The kernel of an homomorphism of Harish-Chandra
The Moduli of Weierstrass Fibriations Over P1 .
The moduli scheme M (0, 2, 4) over IP3.
The Moduli Space of (3,3,3) Trilinear forms.
The moduli space of totally marked degree two rational maps
A rational map ϕ: ℙ¹ → ℙ¹ along with an ordered list of fixed and critical points is called a totally marked rational map. The space of totally marked degree two rational maps can be parametrized by an affine open subset of (ℙ¹)⁵. We consider the natural action of SL₂ on induced from the action of SL₂ on (ℙ¹)⁵ and prove that the quotient space exists as a scheme. The quotient is isomorphic to a Del Pezzo surface with the isomorphism being defined over ℤ[1/2].
The Mordell–Lang question for endomorphisms of semiabelian varieties
The Mordell–Lang conjecture describes the intersection of a finitely generated subgroup with a closed subvariety of a semiabelian variety. Equivalently, this conjecture describes the intersection of closed subvarieties with the set of images of the origin under a finitely generated semigroup of translations. We study the analogous question in which the translations are replaced by algebraic group endomorphisms (and the origin is replaced by another point). We show that the conclusion of the Mordell–Lang...
The multipliers of similitudes and the Brauer group of homogeneous varieties.
The Mumford-Tate group of 1-motives
In this paper we study the structure and the degeneracies of the Mumford-Tate group of a 1-motive defined over . This group is an algebraic - group acting on the Hodge realization of and endowed with an increasing filtration . We prove that the unipotent radical of , which is , injects into a “generalized” Heisenberg group. We then explain how to reduce to the study of the Mumford-Tate group of a direct sum of 1-motives whose torus’character group and whose lattice are both of rank 1....
The normality of closures of conjugacy classes of matrices.
The normality of closures of orbits in a Lie algebra.
The number of points on certain families of hypersurfaces over finite fields
The Number of Rational Quartics on Calabi-Yau Hypersurfaces in Weighted Projective Space P (2,1...).
The Picard Group of a complex quotient variety.