Related papers: On adding a variable to a Frobenius manifold and g…

We construct equivariant vector bundles over quantum projective spaces making use of parabolic Verma modules over the quantum general linear group. Using an alternative realization of the quantized coordinate ring of projective space as a…

Let $X=G/P$ be a partial flag variety, where $G$ is a semi-simple, simply connected algebraic group defined over an algebraically closed field $K$ of positive characteristic. Let $\mathsf{F}\colon X\to X$ be the absolute Frobenius morphism.…

We study the general theory of Frobenius algebras with group actions. These structures arise when one is studying the algebraic structures associated to a geometry stemming from a physical theory with a global finite gauge group, i.e.…

Let $X_0$ be an irreducible smooth projective curve defined over $\overline{\mathbb Q}$ and $f_0 : X_0 \rightarrow \mathbb{P}^1_{\overline{\mathbb Q}}$ a nonconstant morphism whose branch locus is contained in the subset $\{0,1, \infty\}…

Frobenius manifold structures on the spaces of abelian integrals were constructed by I. Krichever. We use D-modules, deformation theory, and homological algebra to give a coordinate-free description of these structures. It turns out that…

As a formulation of 'codimension-two arguments' in invariant theory, we define a (rational) almost principal bundle. It is a principal bundle off closed subsets of codimension two or more. We discuss the behavior of the category of…

This paper studies the homotopy theory of parameterized spectrum objects in a model category from a global point of view. More precisely, for a model category $\mathcal{M}$ satisfying suitable conditions, we construct a relative model…

Consider an anchored bundle $(E,\rho)$, i.e. a vector bundle $E\to M$ equipped with a bundle map $\rho \colon E \to TM$ covering the identity. M.~Kapranov showed in the context of Lie-Rinehard algebras that there exists an extension of this…

We investigate the geometry of a normal bundle equipped with a $(p,q)$-metric, i.e., Riemannian metric of Cheeger-Gromoll type, to the submanifold of a Riemannian manifold. We derive all natural object as the Levi-Civita connection,…

Let $X$ be a smooth projective variety of dimension $n$ over an algebraically closed field $k$ with ${\rm char}(k)=p>0$ and $F:X\to X_1$ be the relative Frobenius morphism. For any vector bundle $W$ on $X$, we prove that instability of…

The purpose of this paper is to put the description of number scaling and its effects on physics and geometry on a firmer foundation, and to make it more understandable. A main point is that two different concepts, number and number value…

The purpose of this paper is to describe several applications of finiteness properties of $F$-finite $F$-modules recently discovered by M. Hochster to the study of Frobenius maps on injective hulls, Frobenius near-splittings and to the…

Consider a closed manifold $M$ immersed in $\R^m.$ Suppose that the trivial bundle $M\times\R^m=TM\otimes \nu M$ is equipped with an almost metric connection $\tilde{\nabla}$ which almost preserves the decomposition of $M\times\R^m$ into…

We compute decomposition of Frobenius push-forwards of line bundles on quadrics into a direct sum of line bundles and spinor bundles. As an application we show when the Frobenius push-forward gives a tilting bundle and we apply it to study…

Let M be a compact Riemannian manifold without boundary and let E be a Riemannian vector bundle over M. If $\Sigma$ denotes the sphere subbundle of E, we look for embeddings of $\Sigma$ into E admitting a prescribed mean curvatures of…

This work uses fiber bundles as a framework to describe some effects of number scaling on gauge theory and some geometric quantities. A description of number scaling and fiber bundles over a flat space time manifold, M, is followed by a…

We use the G-invariant non-degenerate form on the Steinberg module to Frobenius split the cotangent bundle of a flag variety in good prime characteristics. This was previously only known for the general linear group. Applications are a…

Let $X$ be a smooth projective variety over a perfect field $k$ of characteristic $p>0$, and $V$ be a vector bundle over $X$. It is well known that if $X$ is a curve and $V$ is not strongly semistable, then some Frobenius pullback…

The goal of this paper is to introduce the notion of $G$-Frobenius manifolds for any finite group $G$. This work is motivated by the fact that any $G$-Frobenius algebra yields an ordinary Frobenius algebra by taking its $G$-invariants. We…

We study the Fourier-Mukai functor D(Y) -> D(X) induced by the universal family on a fine moduli space Y for simple semihomogeneous vector bundles on an abelian variety X. The main result is that the Fourier-Mukai transform of a very…