Arcs on Determinantal 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.

arXiv comment27 pages. This is part of the author's PhD thesis at the University of Illinois at Chicago. v2: Minor changes. To appear in Transactions of the American Mathematical Society

References in corpus (7)

• Motivic Igusa zeta functions
• Jet Schemes of Locally Complete Intersection Canonical Singularities
• Jet schemes, log discrepancies and Inversion of Adjunction
• Jets via Hasse-Schmidt Derivations
• Motivic integration, quotient singularities and the McKay correspondence
• Exceptional divisors which are not uniruled belong to the image of the Nash map
• Invariants of singularities of pairs

Cited by in corpus (15)

• The arc space of the Grassmannian
• Hilbert series of certain jet schemes of determinantal varieties
• Jet schemes of quasi-ordinary surface singularities
• Standard monomials and invariant theory for arc spaces I: general linear group
• Computing with jets
• The dimension of jet schemes of singular varieties
• On jet schemes of pfaffian ideals
• A Transversality Theorem for some Classical Varieties
• The $F$-pure threshold of a determinantal ideal
• Arc spaces and equivariant cohomology
• Jet schemes and singularities of W^r_d(C) loci
• Test, multiplier and invariant ideals
• On the embedded Nash problem
• Log canonical thresholds of generic links of determinantal varieties
• Jet schemes of toric surfaces (a short version)