The Invariants of Unipotent Radicals of Parabolic Subgroups.
The Irregularities of Hirzebruch's Examples of Surfaces of General Type with c21= 3c2 .
The kernel of an homomorphism of Harish-Chandra
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 multipliers of similitudes and the Brauer group of homogeneous varieties.
The normality of closures of conjugacy classes of matrices.
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.
The quasi-hereditary algebra associated to the radical bimodule over a hereditary algebra
Let Γ be a finite-dimensional hereditary basic algebra. We consider the radical rad Γ as a Γ-bimodule. It is known that there exists a quasi-hereditary algebra 𝓐 such that the category of matrices over rad Γ is equivalent to the category of Δ-filtered 𝓐-modules ℱ(𝓐,Δ). In this note we determine the quasi-hereditary algebra 𝓐 and prove certain properties of its module category.
The scheme of connected components of the Néron model of an algebraic torus.
The strong linkage principle.
The structure of proper rigid groups.
The trace formula for equivariant D-modules and perverse sheaves.
The Two Most Algebraic K3 Surfaces.
The variety of dual mock-Lie algebras
We classify all complex - and -dimensional dual mock-Lie algebras by the algebraic and geometric way. Also, we find all non-trivial complex -dimensional dual mock-Lie algebras.
Théorèmes sur les équations algébriques.
Top-stable and layer-stable degenerations and hom-order
Using geometrical methods, Huisgen-Zimmermann showed that if M is a module with simple top, then M has no proper degeneration such that for all t. Given a module M with square-free top and a projective cover P, she showed that if and only if M has no proper degeneration where M/M ≃ N/N. We prove here these results in a more general form, for hom-order instead of degeneration-order, and we prove them algebraically. The results of Huisgen-Zimmermann follow as consequences from our results....
Torseurs pour les motifs et pour les representations p-adiques potentiellement de type CM.
Trace Formula for Vanishing Cycles of Curves.