6533b821fe1ef96bd127b98c

RESEARCH PRODUCT

Multiple point spaces of finite holomorphic maps

G. Peñafort-sanchisJ. J. Nuño-ballesteros

subject

Multiple pointMathematics - Algebraic GeometryGeneral Mathematics58K20 58K25 58K60 (Primary) 32C15 32G05 (Secondary)010102 general mathematics0103 physical sciencesFOS: Mathematics0101 mathematicsAlgebraic Geometry (math.AG)01 natural sciencesHumanities010305 fluids & plasmasMathematics

description

We show that there exists a unique possible definition, with certain natural properties, of the multiple point space of a holomorphic map between complex manifolds. Our construction coincides with the double point space and the k-th multiple point space for corank one map-germs, due to Mond. We also give some interesting properties of the double point space and prove that in many cases it can be computed as the zero locus of certain quotient of ideals.

yearjournalcountryeditionlanguage
2015-09-16The Quarterly Journal of Mathematics
https://doi.org/10.1093/qmath/haw042