31 research outputs found
Quasi complete intersections and global Tjurina number of plane curves
A closed subscheme of codimension two is a quasi complete
intersection (q.c.i.) of type if there exists a surjective morphism
. We give bounds on deg in function of and , 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
Quasi-complete intersections in P2 and syzygies
Let C \in P2 be a reduced, singular curve of degree d and equation f = 0. Let
\Sigma denote the jacobian subscheme of C. We have 0 -> E -> 3.O ->
I_\Sigma(d-1) -> 0 (the surjection is given by the partials of f). We study the
relationships between the Betti numbers of the module H^0_*(E) and the
integers, d; \tau, where \tau = deg(\Sigma). We observe that our results apply
to any quasi-complete intersection of type (s; s; s).Comment: New version with improved results and references adde