Explores the universe of complex projective varieties, with a focus on their birational classification. This vertical investigates the deep connections between algebraic geometry, commutative algebra, and arithmetic. One of its main goals is to develop innovative algebraic–geometric codes, contributing to information theory.
Led by Eduardo Esteves (IMPA)
Birational classification of complex varieties and holomorphic foliations using a range of techniques, including Commutative Algebra, curve theory and associated moduli spaces, sheaf theory, and geometry in positive characteristic.
Moduli spaces of sheaves on projective varieties of dimensions 1, 2, and 3, as well as freeness criteria for divisors, and applications of these results in algebra and mathematical physics.
Classification of curves over non-geometric fields and the construction of special algebraic–geometric codes; classification of Artinian algebras satisfying the Lefschetz property; and expansion of the connections between commutative algebra and foliation theory.