NettetIn the proof of Theorem 2.1, one considers the whole Hodge locus Lof a vari-ation, instead of that de ned by just one section; this is often called the (integral) Noether-Lefschetz locus. If (V Z;F) is a variation of polarized Hodge structure of weight 2pon a complex manifold S, its integral Hodge locus is the subset of the bundle Fpde ned by
On the Periods of Integrals on Algebraic Manifolds
NettetThe Hodge locus HL(S,V) is the set of points s ∈ San for which the Hodge structure Vs admits more Hodge classes than the very general fiber V s (for us a Hodge class of a pure Z-Hodge structure H = (HZ,F•) is a class in HZ whose image in HC lies in F0HC, or equivalently a morphism of Hodge structures Z(0) → H). It is empty if V contains ... Nettet29. mar. 2024 · In this paper we investigate the geometry of the Zariski-closure of the Hodge locus \text { HL } (S, { {\mathbb {V}}}^\otimes ). Our methods are variational, … chicken apple sausage pasta bake
On the geometric André–Oort conjecture for variations of Hodge …
Nettet29. mar. 2024 · In this paper we investigate the geometry of the Zariski-closure of the Hodge locus \text { HL } (S, { {\mathbb {V}}}^\otimes ). Our methods are variational, hence we only detect the special subvarieties of S for { {\mathbb {V}}} which are of positive period dimension in the following sense: Nettet13. nov. 2024 · and any tangent vector \(t \in T_oB\), the fundamental class [D] deforms as a Hodge class in the direction of t if and only if the image of \(\xi ^t_D \in H^2_D({{\,\mathrm{{\mathcal {O}}}\,}}_X)\) defined in Theorem 1.1 above, maps to zero in \(\mathrm {coker}(\Phi _{(T \subseteq D)})\).. In other words, the topological obstruction … Nettet21. nov. 2024 · PDF This is the announcement of a conjecture on a Hodge locus for cubic hypersurfaces. Find, read and cite all the research you need on ResearchGate chicken apple sausage stuffing