2 problems

0 votes0 replies1 view
Laface–Ugaglia conjecture on special effect varieties in $\mathbb{P}^3$
Laface–Ugaglia conjecture. The special effect varieties for Cremona reduced linear systems in $\mathbb{P}^3$ are lines through two points and quadrics through nine points.
Conjecturesolvedlinear-systems projective-geometry special-effect-varietiesarXiv posted 2 days ago
0 votes0 replies0 views
Numerical special effect conjecture for plane linear systems
Numerical special effect conjecture. The system ${\mathcal{L}}_{2,d}(-\sum_{i=1}^hm_iP_i)$ is special if and only if it is numerically special.
Conjectureopenlinear-systems plane-curves special-effect-varietiesarXiv posted 2 days ago

Laface–Ugaglia conjecture on special effect varieties in P3\mathbb{P}^3P3