16 problems

Let $D$ be a Mumford--Tate domain parameterizing pure, effective, weight $\mathsf{w}$, $Q$-polarized Hodge structures on a finite-dimensional rational vector space $V$. Let…

Let $X$ be a closed oriented $4$-manifold with $b_2^+(X)=1$. The period map sends a Riemannian metric to the self-dual line $H^+$ in the cone $\mathcal{P}$ of elements of positive…

Griffiths conjecture. The period image $\mathlcal P$ is quasi-projective and $\varphi$ is induced by an algebraic morphism; $L$ is ample on $\mathlcal P$; and there exists a Baily–…

BKU atypical Hodge locus conjecture. The following conditions are equivalent: $\mathrm{HL}(S,\mathbb V)_{\mathrm{atyp}}$ is a finite union of maximal atypical special subvarieties;…

Let $\mathcal{M}$ be the moduli space of I-surfaces, let $\widetilde{\mathcal{M}}$ be the natural blowup of the moduli space along the boundary, let…

Let $\mathcal{M}$ be the moduli space of I-surfaces, let $\widetilde{\mathcal{M}}$ be its natural blowup along the boundary strata, and let…

Toroidal compactification conjecture. There is a morphism

Period-preserving involution conjecture. The space $F_{1,1}$ admits a period-preserving birational involution $S\leftrightarrow S'$ such that

Let $\mathbb V$ be as in Theorem mainqsimple, and let $(\mathbf M,D_M)\subsetneq(\mathbf G,D)$ be a strict Hodge sub-datum satisfying … The expected-dimension typical-point conject…

Let $\mathbb V$ be a polarizable $\mathbb Z$-VHS on a smooth, irreducible and quasi-projective variety $S$ over $\mathbb C$. The typical Hodge-locus density conjecture. If…

Let $\mathcal{X}_{10}$ be the moduli space of ordinary Gushel–Mukai threefolds, let $\mathcal{A}_{10}$ be the moduli space of $10$-dimensional principally polarised abelian varieti…

Let $W_0\subset W$ be the base locus of the relevant smooth family, let $p^c\colon W_0\to D^c/\Gamma$ be the period map of the canonical moduli part, and set … Let $\mathcal M^c_W$…

Let $(f:V\to U,\mathcal{L})\in\mathcal{M}_h(U)$ be the polarized family referred to in Theorem, and let $S$ and $T$ be the loci appearing there. Vector-bundle-injection conjecture.…

Let $f:\mathfrak{X}\to S$ be an algebraic family of polarized algebraic manifolds over a quasi-projective manifold $S$, with period map $\Phi:S\to\Gamma\backslash D$ and lifted per…

Period-map conjecture. There is a period map from the moduli space of such marked pairs to $\operatorname{Hom}(f_d^{\perp}/R_L,C)$, and this period map is an isomorphism over a den…

Canonical Brieskorn-lattice Torelli conjecture. The map $BL$ is injective.