Quasi complete intersections and global Tjurina number of plane curves

2019/01/03 by Ellia, Philippe · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1901.00809

Abstract

A closed subscheme of codimension two T ⊂ P² is a quasi complete intersection (q.c.i.) of type (a,b,c) if there exists a surjective morphism O (-a) ⊕ O (-b) ⊕ O (-c) → I _T. We give bounds on deg(T) in function of a,b,c and r, the least degree of a syzygy between the three polynomials defining the q.c.i. As a by-product we recover a theorem of du Plessis-Wall on the global Tjurina number of plane curves and some other related results.

Cited by

• Bourbaki modules and the module of Jacobian derivations of projective hypersurfaces

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