There are several mantras that are chanted during the Ganapathi Homam to invoke the blessings of Lord Ganesha. Some of the common mantras include:

1. Ganapathi Atharva Sheersham: This is a powerful hymn that praises Lord Ganesha and seeks his blessings. It is usually chanted at the beginning of the Homam.
2. Ganapathi Moola Mantra: This is the basic mantra for Lord Ganesha and is chanted to invoke his blessings.
3. Ganapathi Gayatri Mantra: This is a powerful mantra that is chanted to invoke the blessings of Lord Ganesha. It is believed to promote wisdom and knowledge.
4. Om Gam Ganapataye Namaha: This is a powerful mantra for Lord Ganesha that is chanted to remove obstacles and bring success.
5. Vakratunda Mahakaya: This is a popular mantra for Lord Ganesha that is chanted to seek his blessings for success and prosperity.
6. Om Shri Ganeshaya Namaha: This is a simple yet powerful mantra for Lord Ganesha that is chanted to seek his blessings for success and prosperity.

The specific mantras used in the Ganapathi Homam may vary depending on the tradition and the purpose of the Homam. It is important to follow the correct procedures and chants as prescribed by the priest or the trained individual who is performing the Homam.

Here are some slokas that are commonly recited during the Ganapathi Homam:

• Vakratunda Mahaakaaya Suryakoti Samaprabhaa Nirvighnam Kuru Me Deva Sarva Kaaryeshu Sarvadaa

Meaning: O Lord with a curved trunk and a massive body, whose radiance is like that of a million suns, I pray to you to remove all obstacles in all my endeavors.

• Om Gam Ganapataye Namaha

Meaning: Salutations to Lord Ganesha, the remover of obstacles.

• Shuklaambara Dharam Vishnum Shashi Varnam Chaturbhujam Prasanna Vadanam Dhyaayet Sarva Vighna Upashaantaye

Meaning: I meditate on Lord Ganesha, who is clad in white robes, has a moon-like complexion, and four arms. May he remove all obstacles and bestow his blessings upon us.

• Gajananam Bhoota Ganadi Sevitam Kapittha Jambu Phala Sara Bhakshitam Uma Sutam Shoka Vinasha Karanam Namami Vighneshvara Pada Pankajam

Meaning: I bow to Lord Ganesha, who is worshipped by all beings, and who enjoys eating the pulp of kapittha and jambu fruits. He is the son of Goddess Uma and the destroyer of sorrow. I offer my salutations to his lotus feet.

• Vighna Nashanaya Namaha

Meaning: Salutations to Lord Ganesha, the remover of obstacles.

These are some of the slokas that are commonly recited during the Ganapathi Homam. It is important to follow the correct procedures and chants as prescribed by the priest or the trained individual who is performing the Homam.