Samurai swords, specifically katana, are known for their exceptional sharpness due to several factors:

1. High-quality steel: Samurai swords are typically made from high-quality steel, traditionally known as "tamahagane," which is specifically crafted for sword making. Tamahagane is created through a labor-intensive process of smelting and folding multiple layers of iron sand and charcoal to create a homogeneous and high-carbon steel with desirable properties for swordsmithing.
2. Differential hardening: Samurai swords undergo a process called "differential hardening" or "yakiba." This technique involves heating the edge of the blade to a higher temperature and then rapidly quenching it, creating a hardened and sharp cutting edge. The spine of the blade is left relatively softer, providing flexibility and strength.
3. Precision forging and grinding: Samurai swords are meticulously crafted by skilled swordsmiths. The forging process involves hammering, shaping, and repeatedly folding the steel to remove impurities, improve the steel's consistency, and create a fine grain structure. The blade is then carefully ground and polished to achieve the desired shape, edge geometry, and sharpness.
4. Honing and sharpening: Swordsmiths carefully hone and sharpen the blade to achieve a razor-sharp edge. They use various sharpening stones and techniques to refine the cutting edge, ensuring it is keen and capable of slicing through targets effectively.
5. Geometry and design: The geometry of the blade, including the curvature (sori) and the shape of the edge (nagasa), is meticulously designed to optimize cutting performance. The geometry, along with the sharpness of the edge, allows for efficient cutting and minimizes resistance.

It's important to note that the sharpness of a samurai sword is not only for aesthetic or decorative purposes but also to maximize its effectiveness as a weapon. Samurai swords were historically designed to be highly functional tools for combat, enabling precise and lethal strikes.

Proper maintenance and care are necessary to preserve the sharpness of a samurai sword. Regular cleaning, oiling, and avoiding improper usage or impact on hard surfaces can help maintain the blade's sharp edge and overall condition.