3 problems

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Geometric Manin's conjecture on dominance of Manin components
Let $X$ be a Fano variety and $C$ a smooth projective curve. A Manin component is an irreducible component of the relevant morphism space distinguished from exceptional components.…
Conjecturesolvedfano-varieties manin-conjecture moduli-of-mapsarXiv posted 2 days ago
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Expected dimension conjecture for maps to general hypersurfaces in Grassmannians
Let $C$ be a smooth curve of genus $g$ , let $G(r,n)$ be a Grassmannian, and let $X_{\ell}$ be a general hypersurface of degree $\ell$ in $G(r,n)$ with $\ell<n$ . Denote by…
Conjectureopengrassmannians hypersurfaces moduli-of-mapsarXiv posted 2 days ago
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Equivalence of boundedness notions for projective varieties
Boundedness equivalence conjecture. The following are equivalent:
Conjectureopenalgebraic-hyperbolicity boundedness moduli-of-mapsarXiv posted 2 days ago

Geometric Manin's conjecture on dominance of Manin components