Related papers: Twisted forms of commutative monoid structures on …
We study the quantum Hamiltonian reduction for affine superalgebras in the twisted case. This leads to a general representation theory of all superconformal algebras, including the twisted ones (like the Ramond algebra). In particular, we…
We prove that the image of the lifted period map on the universal cover lies in a complex Euclidean space. We also prove that the Teichm\"uller spaces of a class of polarized manifolds have complex affine structures.
We discuss variations of mixed Hodge structure arising from projective morphisms of complex analytic spaces. Then we treat generalizations of Koll\'ar's torsion-free theorem, vanishing theorem, and so on, for reducible complex analytic…
We consider the set of forms of a toric variety over an arbitrary field: those varieties which become isomorphic to a toric variety after base field extension. In contrast to most previous work, we also consider arbitrary isomorphisms…
Aspects of the algebraic structure and representation theory of the quantum affine superalgebras with symmetrizable Cartan matrices are studied. The irreducible integrable highest weight representations are classified, and shown to be…
We use real algebraic geometry to construct an affine $\Lambda$-building $B$ associated to the $\mathbb{F}$-points of a semisimple algebraic group, where $\mathbb{F}$ is a valued real closed field. We characterize the spherical building at…
In this paper we study those submonoids of $\mathbb{N}^d$ which a non-trivial pseudo-Frobenius set. In the affine case, we prove that they are the affine semigroups whose associated algebra over a field has maximal projective dimension…
We study moduli spaces of twisted maps to a smooth pair in arbitrary genus, and give geometric explanations for previously known comparisons between orbifold and logarithmic Gromov--Witten invariants. Namely, we study the space of twisted…
We construct a non-normal affine monoid together with its modules associated with a negative definite plumbed $3$-manifold $M$. In terms of their structure, we describe the $H_1(M,\mathbb{Z})$-equivariant parts of the topological Poincar\'e…
We investigate the arithmetic of algebraic curves on coarse moduli spaces for special linear rank two local systems on surfaces with fixed boundary traces. We prove a structure theorem for morphisms from the affine line into the moduli…
We study here systems of symmetries on $|1|$--graded parabolic geometries. We are interested in smooth systems of symmetries and we discuss non--flat homogeneous $|1|$--graded geometries. We show the existence of an invariant admissible…
In this paper we detail a number of properties of the affine line of a derivator, including a number of morphisms between $\mathbb{D}$ and $\mathbb{A}^1_{\mathbb{D}}$, a monoidal structure on $\mathbb{A}^1_{\mathbb{D}}$ if $\mathbb{D}$ is…
We construct examples of non-isomorphic algebraic vector bundles on the punctured affine space with isomorphic pullbacks to the smooth quadric.
We show that conformal transformations on the generalized Minkowski space $\mathbb{R}^{p,q}$ map hyperboloids and affine hyperplanes into hyperboloids and affine hyperplanes. We also show that this action on hyperboloids and affine…
The polynomial automorphisms of the affine plane over a field K form a group which has the structure of an amalgamated free product. This well-known algebraic structure can be used to determine some key results about the symmetry and…
In this paper, we report several large classes of affine varieties (over an arbitrary field $K$ of characteristic 0) with the following property: each variety in these classes has an isomorphic copy such that the corresponding isomorphism…
The theme of the paper is the use of commutative Frobenius algebras in braided strict monoidal categories in the study of varieties of circuits and communicating systems which occur in Computer Science, including circuits in which the wires…
In this paper, we construct explicitely polynomial automorphisms of affine n-space for certain n. More precisely, we construct algebraic subgroups of the general polynomial group GA_n(k) where k is an arbitrary base ring of characteristic…
We discuss the concepts of fine and coarse moduli spaces in the context of finite dimensional algebras over algebraically closed fields. In particular, our formulation of a moduli problem and its potential strong or weak solution is adapted…
We suggest to compactify the universal covering of the moduli space of complex structures by non-commutative spaces. The latter are described by certain categories of sheaves with connections which are flat along foliations. In the case of…