On divisorial (i) classes
Olivia Dumitrescu and Nathan Priddis
Journal of Singularities
volume 30 (2026), 144-177
Received: 30 August 2025. In revised form: 29 May 2026
Abstract:
In this paper we introduce and study divisorial (i) classes for the blow up of projective space P^n at several points for i in {-1,0,1}. We generalize Noether's inequality, and we prove that all divisorial (i) classes are in bijective correspondence with the orbit of the Weyl group action on one exceptional divisor following Nagata's original approach. Moreover, we prove that the irreducibility condition from the definition of divisorial (i) classes can be replaced by the numerical condition of having positive intersection with all divisorial (-1) classes of smaller degree via the Mukai pairing.
2010 Mathematical Subject Classification:
Primary: 14C20 Secondary: 14C17, 14J70
Key words and phrases:
(-1) curves, (-1) divisors, (-1) classes, Noether's inequality, Mukai pairing
Author(s) information:
Olivia Dumitrescu
University of North Carolina at Chapel Hill
340 Phillips Hall, CB 3250
Chapel Hill, NC 27599-3250
and
Simion Stoilow Institute of Mathematics
Romanian Academy
21 Calea Grivitei Street
010702 Bucharest, Romania
email: dolivia@unc.edu
Nathan Priddis
Brigham Young University
Provo, Utah 84602, US
email: priddis@math.byu.edu