3 problems

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Landsberg–Manivel's rigidity conjecture for the adjoint variety of $\mathrm{SL}_{m+1}(\mathbb{C})$
Let $X$ be the adjoint variety of $\mathrm{SL}_{m+1}(\mathbb{C})$ , viewed in its natural projective embedding. A variety is rigid to order $k$ if its fundamental forms through orde…
Conjectureopenadjoint-varieties projective-differential-geometry rigidityarXiv posted 2 days ago
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The adjoint-variety conjecture for Fano contact manifolds of Picard number one
A Fano contact manifold of Picard number one is a Fano manifold equipped with a contact structure and whose Picard number is one. An adjoint variety is the unique closed orbit of a…
Conjectureopenadjoint-varieties contact-manifolds fano-varietiesarXiv posted 2 days ago
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Conjecture on rectangular Lefschetz collections for adjoint varieties
Let $X$ be the adjoint variety of a simple algebraic group $\mathrm{G}$ over an algebraically closed field of characteristic zero. Adjoint-variety conjecture. If the Dynkin diagram…
Conjectureopenadjoint-varieties derived-categories exceptional-collectionsarXiv posted 2 days ago

Landsberg–Manivel's rigidity conjecture for the adjoint variety of SLm+1(C)\mathrm{SL}_{m+1}(\mathbb{C})SLm+1​(C)