We have completely mapped the globular cluster NGC 1851 with VI CCD photometry, obtaining a CMD for ca. 20500 stars. From the apparent luminosity of the HB we derive a distance modulus (m-M)o=15.44+/-0.20. The presence of 7 supra-HB stars is confirmed. Six of them are identified as evolved descendants from HB progenitors. Synthetic HR diagrams demonstrate that the problem of the HB morphology could be solved by assuming a bimodal efficiency of the mass loss along the RGB. We find evidence that the radial distribution of the blue HB stars is different from that of the red HB and SGB stars. The first measurement of the mean absolute I magnitude for 22 known RR Lyr variables (<M(I)>=0.12+/-0.20 at [Fe/H]=-1.28), is given. We found 7 new RR Lyr candidates (6 ab type and 1 c type), lowering the ratio N(c)/N(ab) to 0.38. From a sample of 25 globular clusters (including NGC 1851) a new calibration for DV(bump,HB) as a function of metallicity is derived, and we find some evidence for an age-metallicity relation among GCs. We identify 13 blue straggler stars, which do not show any sign of variability. The blue stragglers are less concentrated than the SGB stars with similar magnitudes for r>80. Finally, a radial dependence of the LF, a sign of mass segregation, is found. Transforming the LF into a mass function and correcting for mass segregation by means of multi-mass King-Michie models, we find a global MF exponent x(0)=0.2+/-0.3.
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