What is the name of the sculpture with a head and torso above a plain lower section, often featuring male genitals carved at appropriate height?

The sculpture you are referring to is known as a herm. A herm typically consists of a pillar with a bust of a human figure at the top, specifically the head and torso, while the lower part of the sculpture remains plain. The design often includes distinctive features such as male genitals represented at an appropriate height on the pillar, which emphasizes the male form and fertility. Herms were commonly used in ancient Greek and Roman contexts for various purposes, including boundary markers, commemorative monuments, or protective figures at entrances to spaces. Their simplicity and effectiveness in conveying the representation of the human figure made them a popular style in sculpture.

In contrast, the other options represent different concepts. An exedra is an architectural feature often used in gardens or as part of public buildings, usually a semicircular space for seating. An oecus is a type of room or hall within a house, typically used for gathering or dining, and doesn’t reference a specific sculpture style. An arca refers to a chest or box, often used to store valuables or documents, and is unrelated to the form of sculpture described. Therefore, the characteristics outlined strongly align with the nature of a herm.