Fano

Fano is a town and comune in the Marche region of central Italy, situated on the Adriatic coast in the province of Pesaro e Urbino. The town lies roughly midway between Ancona and Rimini and has ancient roots, with its name dating back to Fanum Fortunae, the Roman settlement at the site. Today Fano has a population in the tens of thousands and features a historic center, coastal beaches, and several churches and palaces. The economy combines tourism, agriculture, and small industry, and the city is known for cultural events such as the Carnevale di Fano, one of Italy’s oldest carnivals, which draws visitors from the region.

In mathematics and geometry, Fano is most prominently associated with Italian mathematicians bearing the surname. Gino Fano, an early 20th-century figure in projective geometry, is commemorated by concepts that bear his name. The Fano plane, the smallest finite projective plane, is a foundational object in combinatorial geometry. The term Fano is also used in algebraic geometry to describe Fano varieties, a broad class of algebraic varieties with ample anticanonical bundle, studied for their rich birational and geometric properties. These notions reflect the influence of Gino Fano's work on subsequent developments in the field.

The name Fano also appears as a surname and place-name element in Italian contexts beyond the town itself, reflecting its historical and cultural associations in the region.