A short-arc discharge lamp capable of reducing the likelihood of cracks starting at an end face of a reflection mirror neck unit. Such cracks can be caused by heat generated from the discharge lamp. The short-arc discharge lamp includes a glass reflection mirror having a reflection surface of an even-order function on an inner surface thereof and formed by embossing. The short-arc discharge lamp is arranged with respect to an optical axis of the reflection mirror. A base of the discharge lamp is fixed to an insertion hole in a hollow neck unit formed in a bottom center of the reflection mirror. Furthermore, a base peripheral portion on the inner surface of the insertion hole in the hollow neck unit has a cylindrical shape with a narrow portion formed to extend from the cylindrical shape toward the reflection surface. Finally, an embossed portion extends from the narrow portion toward the reflection surface while diverging to contact the reflection surface.