 

David McKinnon,
Rindra Razafy,
Matthew Satriano, and
Yuxuan Sun
On curves with high multiplicity on P(a,b,c) for min(a,b,c) ≤ 4
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Published: 
July 24, 2021. 
Keywords: 
weighted projective spaces, curves, Ehrhart polynomial, multiplicity. 
Subject: 
14C15, 14F43. 


Abstract
On a weighted projective surface P(a,b,c) with min(a,b,c) ≤ 4, we compute lower bounds for the effective threshold of an ample divisor, in other words, the highest multiplicity a section of the divisor can have at a specified point. We expect that these bounds are close to being sharp. This translates into finding divisor classes on the blowup of P(a,b,c) that generate a cone contained in, and probably close to, the effective cone.


Acknowledgements
The first author and third authors were partially supported by a Discovery Grant from the National Science and Engineering Board of Canada. The second and fourth authors were supported by an Undergraduate Student Research Award from the National Science and Engineering Board of Canada.


Author information
David McKinnon:
University of Waterloo
Department of Pure Mathematics
Waterloo, Ontario N2L 3G1, Canada
dmckinnon@uwaterloo.ca
Rindra Razafy:
University of Waterloo
Department of Pure Mathematics
Waterloo, Ontario N2L 3G1, Canada
rrazafy@uwaterloo.ca
Matthew Satriano:
University of Waterloo
Department of Pure Mathematics
Waterloo, Ontario N2L 3G1, Canada
msatrian@uwaterloo.ca
Yuxuan Sun:
University of Waterloo
Department of Pure Mathematics
Waterloo, Ontario N2L 3G1, Canada
y376sun@uwaterloo.ca

