No sarcasm, no innuendo, just factual discussion. Here goes ........
Hooks sized #6-8 are usually recommended, though not always, for several reasons, but before we get to why there has to be mention of the hooks strength. You may be able to use a regular wire hook to land carp, even quite large ones, but they also tend to straighten or deform enough that a good one is going to come off. Go with forged hooks instead. You will land a larger percentage of fish. Now, we can agree that hook size should be tailored to bait choice, but the size of a fish's mouth at that point loses a great deal of importance at that juncture, especially with small baits like corn or even small boilies or pieces of crawler. Adding to these points, smaller hooks are less noticeable to fish, especially if you are going to go all out and start using hair rigging and the like, which leaves the hook completely exposed to inspection (and also hooks in the lower lip 99% of the time). On a personal note here, I use hair rigs for all my carp, they are quite easy to tie even for fumble-fingered folk like myself. They are not necessary, but personally I recommend them highly. They do require one specialized piece of equipment in order to use them, some sort of baiting "needle", but you can make one by simply straightening out a long shank light wire hook and gluing it to some sort of handle. To use it you push it through whatever bait you're using, catch the loop in your hair rig behind the barb, then push your bait onto the hair. You can use a piece of anything to keep the bait in place by catching it in the loop and pushing the bait back against it.
Chumming, or the ability to do it legally, has no bearing on hook choice whatsoever. None of what you chum is attached to a hook, it's merely free food to get fish to come to where you're fishing and get them in the mood for more, and for carp the initial attraction comes from scent, since they aren't going to see whatever it is you chummed with until they actually get to it. With that in mind, for those who can't legally do it, try making a dough bait in a flavor you like for carp (there are literally dozens you could use right in the grocery store). Add this same flavor to your can of corn. Mold a bit of the dough around your sinker, not the hook, then add a few pieces of corn to the hook. You have a lot of flavor going into the water, but a small attractive bait close by with the hook point exposed so it takes a bite quickly.
This is the first time I've heard anyone make an argument for hook choice based on the water they are fishing, no matter what species. Carp are carp no matter the water they live in, they feed the same way in all of them based on the structure of their mouth, not their living arrangements. While they will feed up off bottom and even from the surface, generally speaking they are most efficient rummaging the bottom for crustaceans, mollusks, and insect larvae. They hoover up what seems like food, sift out the parts that actually are, and the rest either goes out through their gill rakers or is spit directly from their mouth. Once they do that, food items move back towards their throat, where if necessary they use their pharyngeal teeth to crush it before swallowing (think molars in their throat, pretty well describes it). Works the same whether it's a lake, river, or reservoir. Having said all that, I need to ask some questions here. What sort of rig are you fishing, other than a hook, obviously? I don't want to work from assumptions. How large or small a sinker? How much line between the hook and the sinker? Are you fishing on a tight line or a slack line? I ask because the information adds to the discussion.
This is also the first time I have seen deep hooking prevention as a reason for larger hooks, though I may have missed other posts here and elsewhere explaining the logic of it. Fishing with bait is inherently dangerous simply because of its' nature, we're presenting actual food items to fish often in a manner which gives them time, in many instances, to actually decide to swallow what they ate. There are quite a few different ways to avoid it as much as possible, but this is the first instance I have seen that advocates larger hooks as a viable method.