Can a corporation sue me for harm to its reputation?

Yes. In fact, businesses regularly sue for defamation because their economic interests are often tied to their reputations. The Citizen Media Law Project warns bloggers to be especially cautious when publishing negative information about companies, or their products or services, because false, disparaging statements in this context may also give rise to suits alleging violation of fair trade and fair competition laws or impermissible interference with economic advantage or prospective contractual relations. This is particularly the case when the subject of the negative information is a competitor. Note, however, the use of the word “false” in describing these disparaging comments. Journalists, digital or otherwise, may criticize corporations and the way they do business, so long as the authors do so fairly and accurately. Be aware, however, that businesses frequently resort to SLAPPs to intimidate and silence their critics.