On a recent night out in La Spezia, the nearest real city to Monterosso, a friend of mine excitedly pointed out the grattacielo of La Spezia. She was laughing hysterically as we rounded the corner to see it, and after seeing it myself, I figured out why.
Only here can this be considered a grattacielo - literally, like in english, a skyscraper. Grattare is to scrape, cielo is sky.
Buildings in Monterosso are no more then 4 stories, and those are mostly built into hills, so it keeps them from looking tall, or sticking out awkwardly in the sky. This building is completely out of place, especially in the low Ligurian towns, and even in a city like La Spezia. Being the only building reaching towards the stars (even if it's not actually reaching very far) has earned it it's tounge-in-cheek name.
I think it's adorable.