Another not so simple question. Capital gains do effect the AMT. One way that capital gains effect the AMT is the phase-out of the AMT personal exemption. If you are in that "zone" of income, each additional $1.00 of income takes 25¢ away from your personal exemption. This effectively makes more of your income taxable.
The maximum capital gains tax rate of 15% still applies even in the AMT but if you add $1,000 of capital gain income to a taxpayer in that exemption phase-out "zone" in the AMT, the incremental tax on that capital gain is not $150, but $187.50. That is because the $1,000 of additional income takes away $250 of exemption, creating $1,250 more taxable income. At a 15% tax rate, that equals $187.50.
As we have mentioned throughout, additions to income have all kinds of adverse tax effects, so don't be sold on 15% as being the highest rate of tax on capital gains. There is also the effect of phasing out medical deductions, personal exemptions, child credits, education credits and so forth.