I won't reiterate what others have said.
Personally, my mare just doesn't like geldings. She isn't aggressive towards them, but she won't have anything to do with them and won't tolerate them in her space. We have been at 3 barns in less than a year - long story. We were at one barn that separated. That's when I realized she got along with mares fine, but not geldings. Now she is turned out in a HUGE pasture, with mostly mares and I think 1-2 geldings. One gelding believes she is "his" mare, despite her refusal to associate with him, but he didn't give me much problem after he learned that I am the alpha over everyone in that pasture - and I will take "his" mare if I wish.
Thankfully, Amber learned a long time ago that I can be much scarier than any of the pasture bullies she deals with, so horses being foolish around us doesn't bother her, and she trusts me to handle any horses threatening us. So a possessive gelding we can make quick work of.
She is much happier in her 24/7 turnout though, even with mixed genders, than at the same-gender turnout barn that only turned her out for 3 hours (against my instruction)! The pasture is big enough that she doesn't have to feel cramped with the geldings.
Obviously not every gelding-hating mare is as tolerant as mine..."don't bother me, I won't bother you" is her role in the pasture. She likes being with her herd, but she doesn't really get involved in the herd's social 'world'. Kind of complicated, really. She's definitely the dominant mare out there, but she could care less what everyone else is doing, so long as it isn't affecting her.
Case of this - and another point on mare/gelding separation - a new horse, a 4 y/o TB filly, got turned out with their herd. The gelding who is SO possessive over mares was really giving her a hard time trying to dominate her. She ended up going through a fence. She got banged up, but the vet has said she will recover fully. All the horses got involved, except Amber. I was told that she was standing several yards away, standing still, just watching everything. She doesn't make a point to assert herself over a new horse, and really shows no interest in new horses, unless they get in her way...
Cinnamon Whiskey 11 y/o 15hh Chestnut AQHA mare, 2'6 Jumpers