You may be right. Especially with the dark dot. Perhaps there just wasn't enough water flow around the eggs to keep the fungus from growing. I read that fungus is very common on cory eggs, so it is nothing that you did wrong by any means.
I think it is a combination of factors but I'm no expert by any means. One thing that might help would be to get a net-type breeder so that there can be more water-flow. I have noticed that my cories tend to lay eggs near the filter. I noticed this when I had to move the filter from one side of the tank to the other, and the cories switched sides of the tank they laid most of their eggs on. This suggests to me that they like the water flow for their eggs. Byron recommended a net breeder for me when I found these guys in my filter, and it worked well. Of course, they were already past egg-stage, but the water flow is still better than it would be in a plastic-sided breeder.
This is an example of a net breeder. Well, I think that's what it's called. It is a plastic frame with a net around it. The net allows for water to flow but no fish to get in or out.
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I do find that when feeding fry food, I have to put it on the rails though, because the other fish come at it from the bottom and eat it. Here's a picture of the food on the rail.
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Here's a picture of the inside of the net with the cories in it. They are a little older here. I don't actually try to breed these guys. They just volunteered themselves by getting sucked up into the filter and waiting for some sucker (me) to find them and coddle them. I pulled 11 out of the filter the most recent time (that's when I decided that enough was enough and I put a sponge over the intake tube). At any rate, this view is from directly above the box. You can see the fine mesh as well. I like the net breeder overall. I got mine on Amazon if you are thinking about getting one, but I'm sure pet stores would have them too.
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Here is a picture of cory eggs after they have turned that off-white color I told you about. If you see any eggs this color, grab those and put them in a net breeder and see how they do. The eggs below were eaten within a couple of days (I mean, come on, they even look like they're on a little plate!) but this is the "fertile egg" color. If you never see any get this color, you may not have any males or they may be getting eaten before they can become viable. Best of luck to you!!!
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I ordered the net breeder from Amazon last night. It should be here soon. So if it is a water flow issue then that should fix the problem for the next time. I don't know when the next time will be, but at least I will be ready for it.