Classification of Polarized Manifolds of Sectional Genus Two

Abstract

Listen

Translate article

This chapter discusses the classification polarized manifolds of sectional genus two. Line bundles and invertible sheaves are used interchangeably, and are identified with the linear equivalence classes of Cartier divisors. The tensor products of fine bundles are denoted additively, while multiplicative notation is used for intersection products in Chow rings. The chapter presents an assumption that L is an ample line bundle on a compact complex manifold M with dim M = n. Then, the sectional genus g(M, L) of the polarized manifold (M, L) is defined by the formula g(M, L) – 2 = (K + (n – 1)L)Ln−1, where K is the canonical bundle of M.