star wars - Was there a space battle above Geonosis?

Related to my other question here:

We see in the background that there are Republic capital ships that have landed and troops are being disembarked for the fight. A few scenes later, we see Dooku leaving and the Trade Federation ships in orbit around the planet. Did the Republic capital ships have to fight through the Trade Federation ships before they could land?

Answer

There was very little fighting (if any) in space prior to the ground battle at the Battle of Geonosis.

Wookieepedia's Legends article on the First Battle of Geonosis cites some light skirmishing between Jedi/Republic forces and Separatist planetary defenses in the space around Geonosis. The Legends sources for this are the video games Star Wars: The Clone Wars and Star Wars: Jedi Starfighter. For the most part there was little fighting until the ground battle began.

Canon sources do not mention any fighting in space prior to the ground battle.

The reason for the lack of fighting in space is that the Separatists were caught mostly by surprise. The Military Creation Act had been proposed in the Republic Senate but was opposed by a number of senators (including Padme Amidala) and had not passed yet. As far as the Separatists knew, the Republic had no military and therefore Geonosis did not need to be defended from space. The only Separatist who knew about the existence of the clone army was Count Dooku, and that's because he was secretly playing both sides and had ordered the creation of the clone army.

The surprise was so complete that the Separatists' core ships (which are part of the Lucrehulk-class battleships) were on the ground at the start of the battle and and were attacked by SPHA walkers as they attempted to lift off well after the ground battle was underway:

With their core ships on their ground, the Separatists did not have a significant force (if any) of capital ships in orbit around Geonosis prior to the ground battle.