Service interruption on Monday 11 July from 12:30 to 13:00: all the sites of the CCSD (HAL, Epiciences, SciencesConf, AureHAL) will be inaccessible (network hardware connection).
Skip to Main content Skip to Navigation
Journal articles

Continuous functions on the plane regular after one blowing-up

Abstract : We study rational functions admitting a continuous extension to the real affine space. First of all, we focus on the regularity of such functions exhibiting some nice properties of their partial derivatives. Afterwards, since these functions correspond to rational functions which become regular after some blowings-up, we work on the plane where it suffices to blow-up points and then we can count the number of stages of blowings-up necessary. In the latest parts of the paper, we investigate the ring of rational continuous functions on the plane regular after one stage of blowings-up. In particular, we prove a Positivstellensatz without denominator in this ring.
Document type :
Journal articles
Complete list of metadata
Contributor : Goulwen Fichou Connect in order to contact the contributor
Submitted on : Monday, September 29, 2014 - 2:15:33 PM
Last modification on : Friday, May 20, 2022 - 9:04:46 AM
Long-term archiving on: : Tuesday, December 30, 2014 - 11:20:47 AM


Files produced by the author(s)



Goulwen Fichou, Ronan Quarez, Jean-Philippe Monnier. Continuous functions on the plane regular after one blowing-up. Mathematische Zeitschrift, Springer, 2017, 285 (1), pp.287-323. ⟨10.1007/s00209-016-1708-8⟩. ⟨hal-01069575⟩



Record views


Files downloads