Q. Isn't it against the Geneva Convention for the Military to use hollowpoint or fragmenting ammo?
You probably mean the Hague Peace Conference held in July 1899. That was when "bullets that expand or flatten easily in the human body" were first proscribed. The United States was never a signatory to the Hague Peace Conference which meant that not only could the United States use those rounds but also that if the US entered a conflict all the other parties could use them too.
The United States did, however, sign the Hague Convention 1907, Article 23(e) which forbade: "...arms, projectiles, or material (sic) calculated to cause unnecessary suffering." As a result, US snipers used M-118 ammo, a "Match" version of M-80 ball. (7.62×51mm 173-grain solid-tipped boat tail).
In late 1985, the Judge Advocate General wrote an opinion which affirmed that expanding ammo was legal for the US to use in operations "not involving the engagement of the armed forces of another State" (like counter terrorist operations, for example).
In 1990, another opinion permitted the use of the Sierra MatchKing hollowpoint round by US snipers, reasoning that it was not designed to expand or fragment and that the hollowpoint design was a result of the requirements for manufacturing super-accurate bullets.
Then in 1993 Special Operations Command was given the go-ahead by the Judge Advocate General to equip their forces with JHP rounds (Winchester "Black Talon" at the time) for their H&K MK 23 pistols.
Fact: The actual text read: The Undersigned, Plenipotentiaries of the Powers represented at the International Peace Conference at The Hague, duly authorized to that effect by their Governments, Inspired by the sentiments which found expression in the Declaration of St. Petersburg of the 29th November (11th December), 1868, Declare as follows: "The Contracting Parties agree to abstain from the use of bullets which expand or flatten easily in the human body, such as bullets with a hard envelope which does not entirely cover the core, or is pierced with incisions. The present Declaration is only binding for the Contracting Powers in the case of a war between two or more of them. It shall cease to be binding from the time when, in a war between the Contracting Parties, one of the belligerents is joined by a non-Contracting Power.
Fact: Plenipotentiary (n) circa 1656: a person and especially a diplomatic agent invested with full power to transact business.