Krishna Chaturthi is the name for the 19th Tithi (lunar day). It's nature is Khala Prada, which can be interpreted as "cruel, wicked or bad in nature". It's good for using weapons, keeping arms, killing of enemies, arresting actions, poisoning, igniting fire, Atharva Vidya, works related to electricity. No Manglik works should be done as they get destroyed.
Ganesha (Ganapati) is Devata which rules the 4th Tithi of Krishnapaksh (referring to Muhurta Chintamani and Poorva Kalamrita), which makes Chaturthi good for overcoming problems, the destruction of one's enemies, the removal of obstacles and acts of combat. As per Brihat Samhita, Krishna Chaturthi is ruled by Yama and all actions done in respect of Yama are acceptable.
Being Rikta (that can be translated as "empty hands", "scanty", "destitute") and ruled by Shani (Saturn), 4th Tithi of Krishnapaksh is suitable for following works: arresting, poisoning, uses of weapon, surgery, igniting fire. Travelling in any direction is strictly prohibited during Krishna Chaturthi.
During the vedic month Magha Krishna Chaturthi becomes Sompad Tithi, which is considered auspicious for getting success in activities started during this day (Sompad Tithi is connected to Soma, which is a keeper of Amrta, divine Devata nectar of eternal youth).
During the vedic months Pausha and Phalguna Krishna Chaturthi becomes Maasa Shoonya Tithi, which is considered inauspicious in succeeding in works started during this Tithi.
Krishna Chaturthi becomes Daghda Tithi (burned lunar sign) for times when Surya (Sun) goes through Vrishabha (Taurus) or Kumbha (Aquarius). It's considered that Daghda Tithis are inauspicious to start any type of work.