The Alternative Minimum Tax (AMT) is essentially a separate tax system in the United States wit its own set of tax rates and deduction rules, all of which are usually less generous than the regular rules.
In the startup context, an Alternative Minimum Tax issue can occur in the realm of incentive stock options (ISOs). Since the alternative minimum tax rules have no special treatment for incentive stock options, an ISO grantee may be subject to the alternative minimum tax on the exercise of such stock options.