Geometric properties of jet schemes
Shihoko Ishii
TL;DR
This paper explores how geometric properties of jet schemes reflect and influence the singularity characteristics of the underlying base scheme, establishing inheritance of properties like Q-factoriality and canonical singularities.
Contribution
It demonstrates that key properties of jet schemes such as Q-factoriality and being canonical are inherited by the base scheme, linking jet scheme geometry to singularity theory.
Findings
Jet scheme properties are inherited by the base scheme.
Properties like Q-factoriality and canonical singularities transfer from jet schemes to the base.
The work deepens understanding of the relationship between jet schemes and singularities.
Abstract
This paper shows how properties of jet schemes relate to those of the singularity on the base scheme. We will see that the jet scheme's properties of being Q-factorial, Q-Gorenstein, canonical, terminal and so on are inherited by the base scheme.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Nonlinear Waves and Solitons · Algebraic structures and combinatorial models