Final answer:
Cases involving the state of Georgia as a party are automatically heard by Georgia's Supreme Court due to Section 2 Clause 2 of the U.S. Constitution, although the Eleventh Amendment imposes certain limits on such cases.
Step-by-step explanation:
The kind of case that automatically comes before Georgia's Supreme Court is a case involving the state of Georgia as a party, as mandated by Section 2 Clause 2 of the United States Constitution. This constitutional provision is very limited after the Eleventh Amendment, which restricts the types of cases against a state that can be heard in federal courts. Moreover, cases that could automatically trigger the involvement of Georgia's Supreme Court might include those involving high-ranking state officials or certain types of appeals against the state. Criminal cases typically do not automatically come before the Supreme Court; instead, they may be subject to appellate processes. It's also important to note that while Georgia's Supreme Court may hear cases automatically in certain circumstances, most cases come before the U.S. Supreme Court on appeal from lower courts, requiring a writ of certiorari, which must be granted by at least four of the nine Justices.