Related papers: Balanced Superprojective Varieties
We construct a mathematical framework for twisted N=2 supersymmetric topological quantum field theory on a 4-manifold. Supersymmetry in flat space is defined and the twist homomorphism is constructed, giving us a supermanifold that is the…
In this paper, we provide an accessible introduction to the theory of locally convex supermanifolds in the categorical approach. In this setting, a supermanifold is a functor $\mathcal{M}\colon\mathbf{Gr}\to\mathbf{Man}$ from the category…
In physics literature about supersymmetry, many authors refer to "super Minkowski spaces". These spaces are affine supermanifolds with certain distinguished spin structures. In these notes, we make the notion of such spin structures precise…
A model for $n$ superparticles in $(d-n,n)$ dimensions is studied. The target space supersymmetry involves a product of $n$ momentum generators, and the action has $n(n+1)/2$ local bosonic symmetries and $n$ local fermionic symmetries. The…
Derived geometry provides powerful tools to handle non-transverse intersections and singular moduli problems arising in geometry and theoretical physics. While derived algebraic geometry has been extensively developed, classical field…
We introduce and study the notion of plurisubharmonic functions in calibrated geometry. These functions generalize the classical plurisubharmonic functions from complex geometry and enjoy their important properties. Moreover, they exist in…
We show that the superconformal symmetries of the (1,1) sigma model decompose into a set of more refined symmetries when the target space admits projectors $P_{\pm}$, and the orthogonal complements $Q_{\pm}$, covariantly constant with…
We show that the term `superdifferential equation' has been employed in the literature to refer to different types of differential equations with even and odd variables. It is justified on physical and mathematical grounds that a subclass…
The aim of this work is the construction of a "supermanifold of morphisms $X \rightarrow Y$", given two finite-dimensional supermanifolds $X$ and $Y$. More precisely, we will define an object $\underline{SC}^\infty(X,Y)$ in the category of…
A theory of graded manifolds can be viewed as a generalization of differential geometry of smooth manifolds. It allows one to work with functions which locally depend not only on ordinary real variables, but also on $\mathbb{Z}$-graded…
We define symmetric spaces in arbitrary dimension and over arbitrary non-discrete topological fields $\K$, and we construct manifolds and symmetric spaces associated to topological continuous quasi-inverse Jordan pairs and -triple systems.…
We analyse the relationship between the N=2 harmonic and projective superspaces which are the only approaches developed to describe general N=2 super Yang-Mills theories in terms of off-shell supermultiplets with conventional supersymmetry.…
In this paper, we introduce the concepts of m-quasiconvex, originally m-quasiconvex,and generalized m-quasiconvex functionals on topological vector spaces. Then we extend the concept of point separable topological vector spaces (by the…
Extension of symplectic geometry on manifolds to the supersymmetric case is considered. In the even case it leads to the even symplectic geometry (or, equivalently, to the geometry on supermanifolds endowed with a non-degenerate Poisson…
Almost-complex and hyper-complex manifolds are considered in this paper from the point of view of complex analysis and potential theory. The idea of holomorphic coordinates on an almost-complex manifold $(M,\mathbf{J}%)$ is suggested by D.…
We analyze the possibility of defining infinite-dimensional manifolds as ringed spaces. More precisely, we consider three definitions of manifolds modeled on locally convex spaces: in terms of charts and atlases, in terms of ringed spaces,…
The concept of super-wavelet was introduced by Balan, and Han and Larson over the field of real numbers which has many applications not only in engineering branches but also in different areas of mathematics. To develop this notion on local…
We give a survey of the incredibly beautiful amount of geometry involved with the problem of realizing a projective variety as hyperplane section of another variety.
We establish a relation between higher contact-like structures on supermanifolds and the N = 1 super-Poincare group via its superspace realisation. To do this we introduce a vector-valued contact structure, which we refer to as a…
The present paper is an extension of a previous paper written in collaboration with Markus Reineke dealing with quiver representations. The aim of the paper is to generalize the theory and to provide a comprehensive theory of…