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Using light curves from the HATNet survey for transiting extrasolar planetswe investigate the optical broad-band photometric variability of a sample of27,560 field K and M dwarfs selected by color and proper-motion. A total of2120 stars exhibit potential variability, including 95 stars with eclipses and60 stars with flares. Based on a visual inspection of these light curves and anautomated blending classification, we select 1568 stars, including 78 eclipsingbinaries, as secure variable star detections that are not obvious blends. Weestimate that a further ~26% of these stars may be blends with faintervariables, though most of these blends are likely to be among the hotter starsin our sample. We find that only 38 of the 1568 stars, including 5 of theeclipsing binaries, have previously been identified as variables or are blendedwith previously identified variables. One of the newly identified eclipsingbinaries is 1RXS J154727.5+450803, a known P = 3.55 day, late M-dwarf SB2system, for which we derive preliminary estimates for the component masses andradii of M_1 = M_2 = 0.258 +- 0.008 M_Sun and R_1 = R_2 = 0.289 +- 0.007 R_Sun.The radii of the component stars are larger than theoretical expectations ifthe system is older than ~200 Myr. The majority of the variables are heavilyspotted BY Dra-type stars for which we determine rotation periods. Using thissample, we investigate the relations between period, color, age, and activitymeasures, including optical flaring, for K and M dwarfs., finding that many ofthe well-established relations for F, G and K dwarfs continue into the M dwarfregime (Abridged).

A PHOTOMETRIC VARIABILITY SURVEY OF FIELD K AND M DWARF STARS WITH HATNet