So in LA there are two types of annulment:
1. absolutely null, in which case the marriage is void, as a matter of law. This would be for example, bigamy.
2. relatively null, in which case the marriage can be declared judicially void. This would include lack of consent (ie an arranged marriage), one party fundamentally misrepresents themselves, one party is or becomes mentally incapacitated of substantial impairment, one party is unable or unwilling to consummate the marriage.
All of these give rise to an action for annulment.
The idea is that marriage is a contract, and misrepresentation or failure to consummate is a breach of that contract.
More can be read about it here:
A divorce attorney would typically handle the process.
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