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A note on the Pullback Conjecture
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DOI：10.4064/ap241208-1-12.png)
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Abstract
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The problem of whether the pullback of a singular analytic germ via a proper holomorphic self-map germ of (Cn, 0) stays singular dates back to 2007 and has not been solved yet, apart from a number of special cases. In this paper we start with a brief overview of the main advances made so far. Then, we observe that analogous results can be proved globally, for algebraic sets and a proper polynomial map. Secondly, we study the case of proper map germs Cn -> Cm, i.e. with m >= n. We also present some additional results, the first of which is an application of a slightly generalised version of the Giraldo-Roeder reduction. Another one involves Lipschitz geometry and Lipschitz normally embedded sets.
Keywords:
complex analytic sets and germs
proper maps
analytic intersec-tion theory
Lipschitz geometry
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A
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0.3
Papers:
24
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0
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