This page describes alternative designs for the 13 volt VPP power supply that have been contributed by members of the community.
Giuseppe Musciacchio contributed the following circuit based on a MAX629 DC-DC Converter (datasheet) that can be powered directly from the Arduino's 5V supply rail:
This MAX629 can output up to 28V, so use a multimeter on the output and adjust the 220K trimpot for 13V before connecting it to the rest of the PIC programmer circuit. According to the datasheet, a MBR0530L diode can be used in place of the 1N5819 diode.
Valter Fukuoka contributed another 5V-powered circuit based on a MC34063 DC-to-DC Converter (or the equivalent part NJM2360):
For finer control of the output voltage, R1 can be replaced with two resistors and a trimpot in series to exactly select the desired VPP value:
The following breadboard layout was created by Valter which shows the position of the components, including the adjustment trimpot: