site stats

Hodge locus

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 https://swrenovators.com

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

On the algebraicity of the Hodge locus Fields Institute for …

Category:On the algebraicity of the Hodge locus Fields Institute for …

Tags:Hodge locus

Hodge locus

The Noether–Lefschetz locus of surfaces in toric threefolds

Nettet10. feb. 1994 · The Hodge filtration Ft of H (Xt,C), t ∈ U , can be viewed as a variable filtration on the fixed complex vector space H(Xs,C). It varies holomorphically with t. It … NettetWe present a conjecture on the geometry of the Hodge locus of a (graded polarizable, admissible) variation of mixed Hodge structure over a complex smooth quasi-projective base, ...

Hodge locus

Did you know?

NettetHodge locus is also a countable union of algebraic subvarieties of T. In this case, the study of the local Hodge loci V λ is an interesting problem by itself, since variational … NettetLocus was an Inhuman of Attilan and a member of the Royal Guard. Following the escape of Gorgon on Oahu, she was recruited a part of a task force to apprehend her former …

NettetGeometry of the Hodge locus. On the distribution of the Hodge locus, (with B.Klingler and E.Ullmo), arXiv, 2024. Special subvarieties of non-arithmetic ball quotients and Hodge … Nettetgeometers would usually just say that the Hodge locus is a countable union of proper closed algebraic subsets, hence that there are complex points in B(C) out-side the …

NettetThe Hodge locus of α is defined as the projection toT (via the natural map p: FkH2k → T)of the connected component of the locus of Hodge classes passing through α . We … Nettet7. nov. 2024 · Date: Title/Abstract: 11/7/2024. Video: Title: Hodge and Noether-Lefschetz loci Abstract: Hodge cycles are topological cycles which are conjecturally (the millennium Hodge conjecture) supported in algebraic cycles of a given smooth projective complex manifold.Their study in families leads to the notion of Hodge locus, which is also …

Nettet12. jan. 2024 · Abstract. We study the subsets V_k (A) of a complex abelian variety A consisting in the collection of points x\in A such that the zero-cycle \ {x\}-\ {0_A\} is k -nilpotent with respect to the Pontryagin product in the Chow group. These sets were introduced recently by Voisin and she showed that \dim V_k (A) \le k-1 and \dim V_k …

Nettet24. mar. 2024 · For every even number n, and every n-dimensional smooth hypersurface of $${\\mathbb {P}}^{n+1}$$ P n + 1 of degree d, we compute the periods of all its $$\\frac{n}{2}$$ n 2 -dimensional complete intersection algebraic cycles. Furthermore, we determine the image of the given algebraic cycle under the cycle class map inside the … google play card customer supportNettet26. jan. 2024 · The Hodge and Tate conjectures state that Hodge and Tate classes should be classes of algebraic cycles, and therefore make the following predictions about … chicken apple sausage with cabbageNettetOn the distribution of the Hodge locus. G. Baldi, B. Klingler, E. Ullmo; Mathematics. 2024. Given a polarizable Z -variation of Hodge structures V over a complex smooth quasi-projective base S , a classical result of Cattani, Deligne and Kaplan says that its Hodge locus (i.e. the locus … Expand. 13. PDF. google play card egift