Free and nearly free surfaces in $P^3$

Abstract

We define the nearly free surfaces in $P^3$ and show that the Hilbert polynomial of the Milnor algebra of a free or nearly free surface in $P^3$ can be expressed in terms of the exponents. An analog of Saito's criterion of freeness in the case of nearly free divisors is proven and examples of irreducible free and nearly free surfaces are given.

v6: Question 5.16 is replaced by Example 5.17 containing examples kindly provided by Aldo Conca. Question 5.17 is replaced by Remark 5.18. Section 6 is discarded and the references are updated

References in corpus (2)

• Freeness versus maximal global Tjurina number for plane curves
• Nearly free divisors and rational cuspidal curves

Cited by in corpus (7)

• Freeness versus maximal global Tjurina number for plane curves
• On some conjectures about free and nearly free divisors
• Plus-one generated and next to free arrangements of hyperplanes
• Deletion theorem and combinatorics of hyperplane arrangements
• The Hessian polynomial and the Jacobian ideal of a reduced hypersurface in ${\mathbb{P}}^n$
• Ramblings on the freeness of affine hypersurfaces
• Freeness versus maximal degree of the singular subscheme for surfaces in $P^3$