  Using a compilation of Halpha fluxes for 384 star forming galaxies detected
during the VESTIGE survey, we study several important scaling relations for a
complete sample of galaxies in a rich environment. The extraordinary
sensitivity of the data allows us to sample the whole dynamic range of the
Halpha luminosity function, from massive (M*~10^11 Mo) to dwarf systems
(M*~10^6 Mo). This extends previous works to a dynamic range in stellar mass
and star formation rate (10^-4<SFR<10 Mo yr^-1) never explored so far. The main
sequence (MS) relation derived for all star forming galaxies within one virial
radius of the Virgo cluster has a slope comparable to that observed in other
nearby samples of isolated objects, but has a dispersion ~3 times larger. The
dispersion is tightly connected to the available amount of HI gas, with
gas-poor systems located far below objects of similar stellar mass but with a
normal HI content. When measured on unperturbed galaxies with a normal HI gas
content, the relation has a slope a=0.92, an intercept b=-1.57, and a scatter
~0.40. We compare these observational results to the prediction of models. The
observed scatter in the MS relation can be reproduced only after a violent and
active stripping process such as ram-pressure that removes gas from the disc
and quenches star formation on short (<1 Gyr) timescales. This rules out milder
processes such as starvation. This interpretation is also consistent with the
position of galaxies of different star formation activity and gas content
within the phase-space diagram. We also show that the star forming regions
formed in the stripped material outside perturbed galaxies are located well
above the MS relation drawn by unperturbed systems. These HII regions, which
might be at the origin of compact sources typical in rich environments, are
living a starburst phase lasting only <50 Myr, later becoming quiescent
systems.
