Abstract
In this paper, we study the discriminant of a hypersurface in a weighted projective space with isolated singularities. We define the discriminant of a hypersurface in [Formula: see text] with [Formula: see text], and show that it satisfies a smoothness criterion over any commutative ring. A smooth hypersurface of degree [Formula: see text] in the weighted projective three-fold [Formula: see text] is a del Pezzo surface of degree [Formula: see text]. We show that the determinant of the Galois action on the [Formula: see text]-lattice arising from its exceptional curves can be computed via the square roots of the discriminant.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
