  Abridged: The giant radio galaxy M 87 with its proximity, famous jet, and
very massive black hole provides a unique opportunity to investigate the origin
of very high energy (VHE; E>100 GeV) gamma-ray emission generated in
relativistic outflows and the surroundings of super-massive black holes. M 87
has been established as a VHE gamma-ray emitter since 2006. The VHE gamma-ray
emission displays strong variability on timescales as short as a day. In this
paper, results from a joint VHE monitoring campaign on M 87 by the MAGIC and
VERITAS instruments in 2010 are reported. During the campaign, a flare at VHE
was detected triggering further observations at VHE (H.E.S.S.), X-rays
(Chandra), and radio (43 GHz VLBA). The excellent sampling of the VHE gamma-ray
light curve enables one to derive a precise temporal characterization of the
flare: the single, isolated flare is well described by a two-sided exponential
function with significantly different flux rise and decay times. While the
overall variability pattern of the 2010 flare appears somewhat different from
that of previous VHE flares in 2005 and 2008, they share very similar
timescales (~day), peak fluxes (Phi(>0.35 TeV) ~= (1-3) x 10^-11 ph cm^-2
s^-1), and VHE spectra. 43 GHz VLBA radio observations of the inner jet regions
indicate no enhanced flux in 2010 in contrast to observations in 2008, where an
increase of the radio flux of the innermost core regions coincided with a VHE
flare. On the other hand, Chandra X-ray observations taken ~3 days after the
peak of the VHE gamma-ray emission reveal an enhanced flux from the core. The
long-term (2001-2010) multi-wavelength light curve of M 87, spanning from radio
to VHE and including data from HST, LT, VLA and EVN, is used to further
investigate the origin of the VHE gamma-ray emission. No unique, common MWL
signature of the three VHE flares has been identified.
