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Non-linear Group Actions with Polynomial Invariant Rings and a Structure Theorem for Modular Galois Extensions
Non-linear Group Polynomial Invariant Rings
2010/11/24
Let $G$ be a finite $p$-group and $k$ a field of characteristic $p>0$. We show that $G$ has a \emph{non-linear} faithful action on a polynomial ring $U$ of dimension $n=\mathrm{log}_p(|G|)$ such that...
We study the convergence of the K\"ahler-Ricci flow on a compact K\"ahler manifold $(M,J)$ with positive first Chern class $c_1(M;J)$ and vanished Futaki invariant on $\pi c_1(M;J)$. As the applicati...
An Invariant Theory of Spacelike Surfaces in the Four-dimensional Minkowski Space
Invariant Theory Spacelike Surfaces
2010/11/23
We consider spacelike surfaces in the four-dimensional Minkowski space and introduce geometrically an invariant linear map of Weingarten-type in the tangent plane at any point of the surface under con...
Invariant subalgebras of affine vertex algebras
Invariant subalgebras affine vertex algebras
2010/11/15
Let g be a simple Lie algebra of dimension n over C, and let V_k(g) be the universal affine vertex algebra at level k. Suppose that G is a reductive group of automorphisms of V_k(g) for all k in C, an...
Geometric interpretation of simplicial formulas for the Chern-Simons invariant
Geometric interpretation simplicial formulas
2010/11/19
We give a direct interpretation of Neumann's combinatorial formula for the Chern-Simons invariant of a 3-manifold with a representation in PSL(2,C) whose restriction to the boundary takes values in u...