On weak Fano manifolds with small contractions obtained by blow-ups of a product of projective spaces

TL;DR

This paper classifies certain weak Fano manifolds with small contractions created by blow-ups in products of projective spaces, detailing their nef cones and anti-canonical divisor properties.

Contribution

It provides a classification for a specific case of weak Fano manifolds obtained via blow-ups, with explicit descriptions of nef cones and intersection numbers.

Findings

Classification result for a special case of weak Fano manifolds

Explicit description of nef cones

Computed self-intersection numbers of anti-canonical divisors

Abstract

We consider weak Fano manifolds with small contractions obtained by blowing up successively curves and subvarieties of codimension 2 in products of projective spaces. We give a classification result for a special case. In the process of proof, we describe explicitly the structure of nef cones and compute the self intersection numbers of anti-canonical divisors for such weak Fano manifolds.