115 Citations
Non-projected Calabi–Yau supermanifolds over $\mathbb{P}^{2}$
- MathematicsMathematical Research Letters
- 2019
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
- MathematicsUniverse
- 2018
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
- Mathematics
- 2020
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,…
OBSTRUCTION THEORY FOR SUPERMANIFOLDS AND DEFORMATIONS OF SUPERCONFORMAL STRUCTURES
- MathematicsBulletin of the Australian Mathematical Society
- 2017
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
- Physics, MathematicsNew 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
- Mathematics
- 2005
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
- Mathematics
- 2001
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
- Mathematics
- 2021
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…