4 problems

0 votes0 replies0 views
Sato's conjecture for smooth Fano varieties of Picard number one
Sato's conjecture. $X$ is a projective space.
Conjectureopenendomorphisms fano-varieties picard-numberarXiv posted 2 days ago
0 votes0 replies1 view
Moyano et al.'s conjecture on Picard numbers determined by Newton–Okounkov bodies
Moyano et al.'s conjecture. The Picard number of a surface should be determined by its Newton–Okounkov bodies if one allows for infinitesimal flags.
Conjectureopenalgebraic-surfaces newton-okounkov-bodies picard-numberarXiv posted 2 days ago
0 votes0 replies0 views
Mukai's generalized conjecture for Fano manifolds
Bonavero–Casagrande–Debarre–Druel conjecture. One has
Conjecturesolvedfano-manifolds picard-number rational-curvesarXiv posted 2 days ago
0 votes0 replies1 view
The maximal Picard number conjecture for Fano manifolds
Let $X$ be a Fano manifold of dimension $n$ . Let $S_1,\ldots,S_r$ be Del Pezzo surfaces with $\rho_{S_i}=9$ . Maximal Picard number conjecture. … with equality if and only if…
Conjectureopendel-pezzo-surfaces fano-manifolds picard-numberarXiv posted 2 days ago

Sato's conjecture for smooth Fano varieties of Picard number one