The Aluffi Algebras and Free Divisors

• Grant number: 22/09853-5
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: January 01, 2023
• End date: December 31, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Marcos Benevenuto Jardim
• Grantee: Marcos Benevenuto Jardim
• Visiting researcher: Abbas Nasrollah Nejad
• Visiting researcher institution: Institute for Advanced Studies in Basic Sciences (IASBS), Iran
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 18/21391-1 - Gauge theory and algebraic geometry, AP.TEM

Abstract

The Aluffi algebra is an algebraic version of a characteristic cycle of a hypersurface in intersection theory which connects with various themes of commutative algebra. In this research project, first we study the torsion-free Aluffi algebras, the Nash Rees algebra and the Jacobian ideal of projectively embedded curves, the Aluffi algebra of space curves and singular hypersurfaces, the linear type property of the defining ideal of the singular subscheme of affine and projective hypersurfaces and the relation type number for analytic k-algebras and complex space germs as an invariant.Free divisors, which were formally defined and investigated by Saito, play a fundamental role for understanding the structure of non-isolated singularities. For divisors in a projective plane the algebraic side of the theory is given by Simis. In the second part of the project we provide a freeness criteria for complete intersection curves in 3-dimensional projective space. (AU)