Margarida Mendes Lopes
Universidade de Lisboa, Portugal
December 10, 2015
Restrictions on the invariants of irregular surfaces: Algebraic surfaces satisfy relations between their invariants like $c_1^2$ (the first Chern number), $p_g$ (the number of independent global holomorphic 2-forms), the holomorphic Euler characteristic, etc. The irregularity of a complex algebraic surface $S$ is the number $q$ of independent (holomorphic) 1-forms that $S$ possesses and a surface is said to be irregular if $q > 0$.
Universidade de Lisboa, Portugal
December 10, 2015
Restrictions on the invariants of irregular surfaces: Algebraic surfaces satisfy relations between their invariants like $c_1^2$ (the first Chern number), $p_g$ (the number of independent global holomorphic 2-forms), the holomorphic Euler characteristic, etc. The irregularity of a complex algebraic surface $S$ is the number $q$ of independent (holomorphic) 1-forms that $S$ possesses and a surface is said to be irregular if $q > 0$.
For irregular surfaces of general type the existence of 1-forms gives additional constraints on the relations between invariants. The aim of this talk, meant as a survey, is to discuss some of these relations, after introducing the general notions.
Part of the results to be presented are joint work with C. Ciliberto, R. Pardini and G.-P. Pirola.