The 10937p-50's a royal PITA to use with LEDs - you'd be far better off chucking them or it back in the parts bin and either using it with a VFD or, if you must drive starburst LEDs, using a string of 74HC595 shift registers and a handful of MOSFETs (or TPIC6C594 power shift registers) and segment limiting resistors, all run from a single positive supply, with the Arduino providing the segment pattern for each character.
However if you *MUST* use it, possibly for a LED conversion of an existing VFR display, a VFD has active high character grids and segment anodes but a starburst LED display has either active high character anodes and active low segment cathodes if its common anode, or visa-versa if its common cathode.
A 10937p-50 is only good for up to 20mA of segment or character drive, so if you are using it with starburst LEDs, it strongly favours using common cathode characters, with a NPN transistor for each cathode so it can sink the worst case 200 mA of a character with ten segments on. Each transistor needs a base resistor to limit the base current and each segment anode needs a current limiting resistor to stay under the 10937p-50's 20mA output rating. You could use ULN2003 or ULN2803 ICs (depending on the number of characters you need) for a reduced parts count solution with all base resistors integrated.
If you are stuck with common anode LED characters, you'll need a NPN emitter follower on each 10937p-50 ADx pin to get enough current, and you'll still need 14 or 16 inverting drivers for the segment cathodes, + resistors to limit the segment currents to whatever the display is rated for. One could use 14 or 14 discrete NPN common emitter transistors + base resistors but the parts count is fairly ridiculous so using 2x ULN2803 or ULN2003 is preferable. Due to the voltage levels involved a 74HC14 is useless. In all cases, to minimise dissipation in the segment resistors, unless you are driving blue LEDs or ones with multiple series dies per segment, the ULN2803 or ULN2003 chip's common emitter pin (GND) should go to 0V not your -10V 10937p-50 Vdd supply.