Some examples of log Fano structures on blow-ups along subvarieties in products of two projective spaces

TL;DR

This paper investigates which blow-ups along subvarieties in products of two projective spaces are log Fano, providing partial classifications and explicit boundary divisors.

Contribution

It offers a partial classification of log Fano structures on blow-ups in products of two projective spaces, including explicit boundary divisors.

Findings

Nef cones of certain blow-ups are described.

Partial classification of log Fano blow-ups achieved.

Explicit boundary divisors provided for examples.

Abstract

We consider the problem to determine which blow-ups along subvarieties in products of two projective spaces are log Fano. By describing the nef cones of such blow-ups with special centers, we give a partial classification result. For each example, explicit boundary divisors are also given.