Colloquium abstracts

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. 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.