Invariant Grassmannians and a K3 surface with an action of order 1922

Given a complex vector space \(V\) of finite dimension, its Grassmannian variety parametrizes all subspaces of \(V\) of a given dimension. Similarly, if a finite group \(G\) acts on \(V\), its invariant Grassmannian parametrizes all the \(G\)-invariant subspaces of \(V\) of a given dimension. Based...

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Bibliographic Details
Published in:arXiv.org 2024-04
Main Author: Muller, Stevell
Format: Article
Language:English
Subjects:
Algorithms
Existence theorems
Gaussian elimination
Group theory
Online Access:Get full text
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Summary:Given a complex vector space \(V\) of finite dimension, its Grassmannian variety parametrizes all subspaces of \(V\) of a given dimension. Similarly, if a finite group \(G\) acts on \(V\), its invariant Grassmannian parametrizes all the \(G\)-invariant subspaces of \(V\) of a given dimension. Based on this fact, we develop an algorithm for computing \(G\)-invariant projective varieties arising as an intersection of hypersurfaces of the same degree. We apply the algorithm to find a projective model of a polarized K3 surface with a faithful action of \(T_{192}\rtimes \mu_2\) and some further symmetric K3 surfaces with a degree 8 polarization.
ISSN:2331-8422