Triggers are more important to Fan Fiction than to original works. Most fanfic readers have developed finely honed Mary Sue detectors. Many of these detectors are tuned to specific fandoms. An original character behaving in one way might not be a problem for one fandom, but in another, it would instantly drive a reader away, screaming "Mary Sue!" the whole while.
However, there is also trust. If an author can get a reader past the first few chapters (assuming the work is that long), then she may be able to start doing these kinds of things. Once a reader trusts the author, the reader is more likely to accept unusual things from her.
The kinds of triggers are wide and varied across fandoms. But there are certain almost universal triggers.
• The Big One: A lot of examples on this page can be summed up as "Your character must fit within the established world". Don't create a special character to your personal liking and just corkscrew her into a story; you must cultivate her out of the world you're writing. It is possible to do both at once but you should never ask yourself "What would be a cool character?" before you ask yourself "What would be a plausible character?"
• Entitlements. If your original character starts getting things, whether actual possessions or just respect, from actual canon characters too soon after his or her introduction, this will have readers leaving in droves. Even if there is some explanation. Avoid this until some level of trust is formed.
• Violations of canon. Every canon has rules. If a character starts breaking the rules, readers are going to call Mary Sue very fast, unless there's a really good explanation that is given immediately. Original Villains might be able to get away with it so that they are more of a threat, but certainly not a new hero.
• Back storying in an original character. This is always suspicious to the cynical fanfic reader, especially if it's a romantic relationship. Speaking of which:
Romancing canon characters. If the story is all about an original character romancing a canon character, people are generally going to call Mary Sue on that. And those who don't certainly will if a canon (or widely-accepted Fanon) relationship is broken up to do it. If any romance is going to take place, it needs to be relevant to the overall plot and contribute to character development, and it can't overwhelm the rest of the narrative. Don't say your OC is married with 3 children to a canon character right off the bat of the story; that only raises more questions that you may or may not want to bother with for the story.
• Overtly flowery descriptions of original characters, as opposed to rather bland descriptions of the canon characters. Most Mary Sue-based fanfiction is poorly written, and thus will contain lavish descriptions of original characters. Avoid doing this early on in a story; either lavishly describe all of the characters in a story, or none of them. Don't split that (unless the writing is in a specific point-of-view that would entail such lavish description).
•Being better than canon characters. If this is not in everything your characterdoes, but only in a few things that the canon character doesn't land top-classin, this is generally not a Sue thing. If your super-amazing OC can run fasterthan Sonic, can fly for longer than Tails, is stronger than Knuckles, issmarter than Dr. Eggman, can use Chaos Control like Shadow, and comes withpsychokinesis like Silver and pyrokinesis like Blaze, that will ring a lot ofalarm bells with your readers. If somebody is canonically the best at what theydo, your audience will be hard-pressed to accept anybody being better than them.
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How to not write a Mary Sue
RandomA Mary Sue is an idealized and seemingly perfect fictional character. These characters are often irritating and cringe worthy. This book will tell everything about identifying a Mary Sue and how to avoid them.