The minimal exponent of cones over smooth complete intersection projective varieties

TL;DR

This paper calculates the minimal exponent of affine cones over smooth complete intersection projective varieties, providing bounds and extending results to weighted homogeneous cases using advanced resolution techniques.

Contribution

It introduces new bounds for the minimal exponent of affine cones over smooth complete intersections, including weighted cases, using factorizing resolutions.

Findings

Upper bound for minimal exponent established

Lower bound derived via strong factorizing resolution

Results extend to weighted homogeneous settings

Abstract

We compute the minimal exponent of the affine cone over a complete intersection of smooth projective hypersurfaces intersecting transversely. The upper bound for the minimal exponent is proved, more generally, in the weighted homogeneous setting, while the lower bound is deduced from a general lower bound in terms of a strong factorizing resolution in the sense of Bravo and Villamayor.