A Gauss-Bonnet theorem for motivic cohomology.
A general embedding theorem in formal geometry
A general Hilbert-Mumford criterion
Let a reductive group act on an algebraic variety . We give a Hilbert-Mumford type criterion for the construction of open -invariant subsets admitting a good quotient by .
A generalisation of the Cassel-Tate pairing.
A generalization of class formation by using hypercohomology.
A generalization of formal schemes and rigid analytic varieties.
A generalization of Jacobi's derivative formula to dimension two.
A Generalization of Kodaira-Ramanujam's Vanishing Theorem.
A Generalization of Kodaira's Embedding Theorem.
A generalization of Lichtenbaum's theorem on the cohomological dimension of algebraic varieties.
A generalization of Mathieu subspaces to modules of associative algebras
We first propose a generalization of the notion of Mathieu subspaces of associative algebras , which was introduced recently in [Zhao W., Generalizations of the image conjecture and the Mathieu conjecture, J. Pure Appl. Algebra, 2010, 214(7), 1200–1216] and [Zhao W., Mathieu subspaces of associative algebras], to -modules . The newly introduced notion in a certain sense also generalizes the notion of submodules. Related with this new notion, we also introduce the sets σ(N) and τ(N) of stable...
A generalization of Mumford's geometric invariant theory.
A generalization of the Chowla-Selberg formula.
A generalized Bloch' s theorem and the hyperbolicity of the complement of an ample divisor in an Abelian variety.
A generating function for fatgraphs
A genericity theorem for algebraic stacks and essential dimension of hypersurfaces
We compute the essential dimension of the functors Forms and Hypersurf of equivalence classes of homogeneous polynomials in variables and hypersurfaces in , respectively, over any base field of characteristic . Here two polynomials (or hypersurfaces) over are considered equivalent if they are related by a linear change of coordinates with coefficients in . Our proof is based on a new Genericity Theorem for algebraic stacks, which is of independent interest. As another application of the...
A geometric algorithm for the output functional controllability in general manipulation systems and mechanisms
In this paper the control of robotic manipulation is investigated. Manipulation system analysis and control are approached in a general framework. The geometric aspect of manipulation system dynamics is strongly emphasized by using the well developed techniques of geometric multivariable control theory. The focus is on the (functional) control of the crucial outputs in robotic manipulation, namely the reachable internal forces and the rigid-body object motions. A geometric control procedure is outlined...
A geometric application of Nori’s connectivity theorem
We study (rational) sweeping out of general hypersurfaces by varieties having small moduli spaces. As a consequence, we show that general -trivial hypersurfaces are not rationally swept out by abelian varieties of dimension at least two. As a corollary, we show that Clemens’ conjecture on the finiteness of rational curves of given degree in a general quintic threefold, and Lang’s conjecture saying that such varieties should be rationally swept-out by abelian varieties, contradict.
A geometric approach to the Jacobian Conjecture in ℂ²
We consider polynomial mappings (f,g) of ℂ² with constant nontrivial jacobian. Using the Riemann-Hurwitz relation we prove among other things the following: If g - c (resp. f - c) has at most two branches at infinity for infinitely many numbers c or if f (resp. g) is proper on the level set (resp. ), then (f,g) is bijective.
A geometric description of Hazama's exceptional classes
Sia una varietà abeliana complessa di tipo Mumford. In queste note daremo una descrizione esplicita delle classi eccezionali in trovate da Hazama in [Ha] e le descriveremo geometricamente usando la grassmaniana delle rette di .