Galoitica: Journal of Mathematical Structures and Applications
Journal DOI
2834-5568ISSN (Online)
Volume 4 , Issue 2 , PP: 24-30, 2023 | Cite this article as | XML | Html | PDF
Nader Taffach 1 *
Doi: https://doi.org/10.54216/GJMSA.040202
The problem of the existence and construction of a resolution of singularities is one of the central questions of algebraic geometry. In this paper, we study this problem in connecting with the quotients for . It is known that the action of on its Lie algebra is corresponding to the action of on . As a result of this action, it will be an invariant ring, which determines the quotients for . This paper is devoted to studying the singularity of these quotients. We write this singularity as a matrix with interesting features such as, for example, its quadratic is a zero matrix and its rank is less than or equal to 1. Therefore, in this paper, we reduce the studying of the singularity of the quotients of , which is a hard problem, to the studying of a matrix of invariants which is an easy problem.
Singularities , Lie algebra , Lie groups , symplectic doubling , quotients
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