• Corpus ID: 115554391

Gauge fields and complex geometry

  title={Gauge fields and complex geometry},
  author={I︠u︡. I. Manin},
Non-projected Calabi–Yau supermanifolds over $\mathbb{P}^{2}$
We start a systematic study of non-projected supermanifolds, concentrating on supermanifolds with fermionic dimension 2 and with the reduced manifold a complex projective space. We show that all the
Non-Projected Supermanifolds and Embeddings in Super Grassmannians
In this paper we give a brief account of the relations between non-projected supermanifolds and projectivity in supergeometry. Following the general results (L. Sergio et al., 2018), we study an
The Unifying Double Complex on Supermanifolds
We unify the notions of differential and integral forms on real, complex and algebraic supermanifolds. We do this by constructing a double complex resulting from a triple tensor product of sheaves,
Supergeometry of Π-projective spaces
Regarding (i), this problem was first studied by Eastwood and LeBrun in [3], where the space of obstructions to extending a thickening of a given order was identified. We present in this thesis
Supergeometry in Mathematics and Physics
  • M. Kapranov
  • Physics, Mathematics
    New Spaces in Physics
  • 2015
This is a chapter for a planned collective volume entitled "New spaces in mathematics and physics" (M. Anel, G. Catren Eds.). The first part contains a short formal exposition of supergeometry as it
On the Origin of the BV Operator on Odd Symplectic Supermanifolds
Differential forms on an odd symplectic manifold form a bicomplex: one differential is the wedge product with the symplectic form and the other is de Rham differential. In the corresponding spectral
Semiinfinite symmetric powers
We develop a theory of measures, differential forms and Fourier tramsforms on some infinite-dimensional real vector spaces by generalizing the following two constructions: (a) The construction of
Conformal maps in higher dimensions and derived geometry
By Liouville’s theorem, in dimensions 3 or more conformal transformations form a finite-dimensional group, an apparent drastic departure from the 2-dimensional case. We propose a derived enhancement
Supersymmetry and the formal loop space