TL;DR
This paper investigates the structure of arc spaces and jet schemes of generic determinantal varieties, providing explicit computations of their irreducible components, log canonical thresholds, and zeta functions.
Contribution
It introduces a group action-based decomposition of arc spaces, enabling new calculations of geometric invariants for determinantal varieties.
Findings
Computed the number of irreducible components of jet schemes
Determined log canonical thresholds for determinantal varieties
Calculated topological zeta functions associated with these varieties
Abstract
We study arc spaces and jet schemes of generic determinantal varieties. Using the natural group action, we decompose the arc spaces into orbits, and analyze their structure. This allows us to compute the number of irreducible components of jet schemes, log canonical thresholds, and topological zeta functions.
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