Negative curves on blowups of weighted projective planes P(a,b,c)

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On this webpage, you can search for negative curves on blowups of weighted projective planes $\mathbb{P}(a,b,c)$ at a general nonsingular point for $0 < a < b < c \le 100$ and $a,b,c$ pairwise coprime.

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This compares S² and abc, where S = a+b+c.

Related search programs and code

This website accompanies the paper "Negative curves on blowups of weighted projective planes" and is based on several MAGMA programs. Download the files below.

Riemann–Roch contributions
Contribution(r,[a,b]) and MakeCon(a,b,c)
Download
Deficiency 0 search program
MAGMA program for negative curves of deficiency 0
Download
Deficiency 1 (and higher): programs and data
Search programs, output data, and verification files
General search
Outputs 1–3
Deficiency 1 output Deficiency 2 output Deficiency 3 output
Skipping cases Irreducibility — Thm. 4.4 Laurent translation — Rem. 4.5 X(9,10,13) — deficiencies 1–10

Results

P[a,b,c] coprime? status degree mult.