  We present results of gasdynamics+N-body constrained cosmological simulations
of the Local Supercluster region (LSC; about 30/h Mpc around the Virgo
cluster), which closely mimic the real Universe within 100 Mpc by imposing
constraints from Mark III catalog of galaxy peculiar velocities. The
simulations are used to study the properties and possible observational
signatures of intergalactic medium in the LSC region. We find that, in
agreement with previous unconstrained simulations, about 30% of the gas in this
region is in the warm/hot phase at T~10^5-10^7 K, and about 40% in the diffuse
phase at T<10^5 K in low-density regions. The best prospects for detection of
the warm/hot intergalactic medium of the LSC located in filaments and in the
vicinity of virialized regions of groups and clusters are through absorption in
resonant lines of OVII and OVIII in soft X-rays and in the OVI doublet in UV.
If intergalactic gas in filaments (rho/<rho>~ 1-10) is enriched to typical
metallicities of >0.05, the column densities of OVI, OVII, and OVIII along a
random line of sight near the North Galactic Pole, especially near the
supergalactic plane, have a significant probability to be in the range
detectable by the current (FUSE,XMM) and future (Constellation-X) instruments.
(Abridged)
