Vector bundles on projective varieties

• Grant number: 14/19676-7
• Support Opportunities: Regular Research Grants
• Start date: November 01, 2014
• End date: January 31, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Simone Marchesi
• Grantee: Simone Marchesi
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

This research project focuses on the study of particular families of vector bundles on projective varieties.The first topic consists in the generalization of the concept of Tango bundles, defined until now only for projective spaces and grassmannians, for quadric hypersurfaces. After obtaining the generalization, we will study the usual properties of vector bundles for this particular family.The second topic consists in the study of bundles defined as the cohomology of a monad. In particular, we will study orthogonal instanton bundles, describing their moduli spaces; Buchsbaum bundles, focusing on the strong relation they have with instanton bundles; and the existence of monads for algebraic varieties in general, something only known for projective spaces until now.After that, we will study the curves whose canonical model lives in a scroll. We will use vector bundles techniques to define the scroll and also to define the curve in the particular case the curve has codimension two.Finally, we will define the concept of regularity for coherent sheaf on projective varieties, relating such concept with the existence of a particular resolution of the sheaf. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

FRANCO, EMILIO; JARDIM, MARCOS; MARCHESI, SIMONE. Branes in the moduli space of framed sheaves. BULLETIN DES SCIENCES MATHEMATIQUES, v. 141, n. 4, p. 353-383, JUN 2017. (12/16356-6, 15/06696-2, 14/14743-8, 14/19676-7)