One higher dimensional analog of jet schemes

Details One higher dimensional analog of jet schemes One higher dimensional analog of jet schemes

2006-08-25

arxiv.org/abs/math/0608633v1

Mathematics

Algebraic Geometry

14 pages, this is part of the author's PhD thesis at the University of Michigan

Scientific paper

We develop the theory of truncated wedge schemes, a higher dimensional analog of jet schemes. We prove some basic properties and give an irreducibility criterion for truncated wedge schemes of a locally complete intersection variety analogous to Musta\c{t}\v{a}'s for jet schemes. We show that the reduced subscheme structure of a truncated wedge scheme of any monomial scheme is itself a monomial scheme in a natural way by explicitly describing generators of each of the minimal primes of any truncated wedge scheme of a monomial hypersurface. We give evidence that the irreducible components of the truncated wedge schemes of a reduced monomial hypersurface all have multiplicity one.

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