We present astrometric very long baseline interferometry (VLBI) studies of
AGB stars. To understand the properties and evolution of AGB stars, distances
are an important parameter. The distribution and kinematics of their
circumstellar matter are also revealed with the VLBI method. We used the VERA
array to observe 22\,GHz H2βO masers in various subclasses of AGB stars.
Parallaxes of the three OH/IR stars NSV17351, OH39.7+1.5, IRCβ30363, and
the Mira-type variable star AW~Tau were newly obtained. We present the
circumstellar distribution and kinematics of H2βO masers around NSV17351. The
absolute magnitudes in mid-infrared bands of OH/IR stars with very long
pulsation periods were investigated and a period-magnitude relation in the WISE
W3 band, MW3β=(β7.21Β±1.18)logP+(9.25Β±3.09), was found
for the Galactic AGB stars. The VLBI is still a powerful tool for parallax
measurements of the Galactic AGB stars surrounded by thick dust shells.Comment: 24 pages, 8 figures, Proceedings of the IAU symposium 376, At the
cross-roads of astrophysics and cosmology Period luminosity relations in the
2020