In the early 1980-ies I. Skornyakov and I proved that a two-sided complex supergrassmannian is not superprojective.
This demonstrated that the role of supergrassmannians in algebraic supergeometry cannot be the same as the role of grassmannians in algebraic geometry. In particular, it motivated the sudy of embeddings of one supergrassmannian into another supergrassmannian.This study has been...
In geometry, the notion of a covering space is classical and well estab-
lished. A familiar example is the universal covering: p : ℝ → S¹, given by
t ↦ exp(it). Analogous constructions also appear in algebra, for instance
in the theory of modules over rings, where one encounters flat or torsion-
free coverings. Despite arising in different contexts, these coverings share a
common...
One of the most celebrated and far-reaching achievements in algebraic geometry is the concept of (perfect) obstruction theory introduced by Behrend and Fantechi. Roughly, this amounts to replacing unbounded cotangent complexes of (very singular) stacks with smaller complexes in order to produce and compute numerical invariants.
In this talk, we describe how this machinery can be generalized...
In this talk I will discuss how Verdier–Poincaré duality specializes to families of supermanifolds in a relative setting. I will then show how this framework yields a genuinely supergeometric (and mathematically rigorous) formulation of supergravity. In particular, it provides a conceptual bridge between the component, geometric, and superspace approaches, clarifying their equivalence as...
We introduce superstacks and describe some of their basic features. As an example the superstack of coherent sheaves on a superprojective superscheme is constructed. A description of its bosonic reduction is given
According to a proposal by Yuri Manin, we want to show that the super Mumford form is the natural measure for the perturbative computation of the string scattering amplitudes.
Starting from a formula provided by A. Voronov in 1988, we show how to get an expression for it in super-coordinates, which correctly reproduces the tree-level amplitudes for Neveau-Schwarz states, without the need to...
I will introduce the notion stable map from a SUSY curve to a fixed target superscheme and study their moduli space, which is a Deligne-Mumford superstack.
