Soft noncommutative schemes via toric geometry and morphisms from an Azumaya scheme with a fundamental module thereto  (Dynamical, complex algebraic) Dbranes on a soft noncommutative space
Abstract
A class of noncommutative spaces, named `soft noncommutative schemes via toric geometry', are constructed and the mathematical model for (dynamical/nonsolitonic, complex algebraic) Dbranes on such a noncommutative space, following arXiv:0709.1515 [math.AG] (D(1)), is given. Any algebraic CalabiYau space that arises from a complete intersection in a smooth toric variety can embed as a commutative closed subscheme of some soft noncommutative scheme. Along the study, the notion of `soft noncommutative toric schemes' associated to a (simplicial, maximal cone of index $1$) fan, `invertible sheaves' on such a noncommutative space, and `twisted sections' of an invertible sheaf are developed and Azumaya schemes with a fundamental module as the worldvolumes of Dbranes are reviewed. Two guiding questions, Question 3.12 (soft noncommutative CalabiYau spaces and their mirror) and Question 4.2.14 (generalized matrix models), are presented.
 Publication:

arXiv eprints
 Pub Date:
 August 2021
 arXiv:
 arXiv:2108.05328
 Bibcode:
 2021arXiv210805328L
 Keywords:

 Mathematics  Algebraic Geometry;
 High Energy Physics  Theory;
 Mathematics  Differential Geometry;
 Mathematics  Symplectic Geometry;
 14A22;
 14A15;
 14M25;
 81T30
 EPrint:
 D(15.1)/NCS(1): 33+2 pp, 3 figures