2025/04/30 by Rodríguez, Abraham del Valle
#14F40 (Secondary) #32S05 #32S25 (Primary) #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.2504.21834
In 2002, it was conjectured that a free divisor satisfying the so-called Logarithmic Comparison Theorem (LCT) must be strongly Euler-homogeneous. Today, it is known to be true only in ambient dimension less or equal than three or assuming Koszul-freeness. Thanks to our advances in the comprehension of strong Euler-homogeneity, we are able to prove the conjecture in the following new cases: assuming strong Euler-homogeneity on a punctured neighbourhood of a point; assuming the divisor is weakly Koszul-free; for ambient dimension n=4; for linear free divisors in ambient dimension n=5. We also refute a conjecture that states that all linear free divisors satisfy LCT and are strongly Euler-homogeneous.