Is hodge bundle ample
WebHodge bundle becomes nef, and the non-ample part of the nef Hodge bundle actually comes from a constant abelian variety. In x3.3, we discuss the possibility of generalizing … Webthe Hodge decomposition for compact, closed K ahler manifolds, a canonical decomposition of each de Rham cohomology space with complex coe cients into Dolbeault cohomology …
Is hodge bundle ample
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WebThis exposition of Hodge theory is a slightly retooled version of the author’s Harvard minor thesis, advised by Professor Joe Harris. Contents 1. Introduction 1 2. Hodge Theory of Compact Oriented Riemannian Manifolds 2 2.1. Hodge star operator 2 2.2. The main theorem 3 2.3. Sobolev spaces 5 2.4. Elliptic theory 11 2.5. Web9. For the purposes of this question, let the Hodge bundle λ be the bundle on a fibration of abelian varieties X → B with fiber over b ∈ B the space of 1-forms on X b, or the pullback to B along the zero section of the sheaf of relative differentials. The most interesting examples are when B is M g or A g, and the fibrations are the ...
WebIn addition to the Hodge line bundle Λe, natural line bundles for the pair (B,Z) include: the normal bundles [Zi] = NZ i/B, with Zi the irreducible components of Z, and the log … Webthat the Hodge bundle A is ample. By R ossler’s result, Theorem1.2is a consequence of Theorem1.1. In fact, it su ces to note the fact that any k-morphism from P1 k to an abelian …
WebMar 1, 2016 · Then the Hodge bundle is by definition ⁎ This line bundle is ample on . In an upcoming paper by the author and T. Wedhorn, it is proved that this line bundle admits a canonical global section, a generalized Hasse invariant, which vanishes exactly outside the μ -ordinary locus [8, Theorem 4.12].
WebHacon’s proof using the Fourier-Mukai transform and some results of mixed Hodge theory (Kollar’s vanishing theorem) and we left this as a blackbox. Actually the most important thing is GV sheaf, as the last section in this blog.
WebSubvarieties with ample normal bundle share many interesting geometric properties with ample divisors (see e.g., [6] or [9]). For example, for every coherent sheaf F, the cohomology ... Theorems 1 and 3 follow directly from the Hodge index theorem. (ii) If Y is a complete intersection, or more generally, a transverse intersection of subva ... data link credit card machinesWebConsequence of the Hodge index theorem. Ask Question Asked 8 years, 6 months ago. Modified 8 ... but not linear equivalent. In addition, the corresponding line bundle $\mathscr L_1 := \mathscr L_{H_1}$ shall be very ample but $\mathscr L_2 :=\mathscr L_{H_2}$ not. ... Because a divisor on a smooth algebraic curve is ample iff it has positive ... martinho lutero biografiaWebNov 12, 2015 · Those with self-intersection $0$ define an elliptic fibration and those with positive self-intersection are ample. This implies that any nef and big divisor is ample. So we obtain: Claim A K3 surface admits a nef and big but not ample divisor if and only if it contains a smooth rational curve. data link control in computer networkWebthe classical Lefschetz theorems for line bundles to the normal case. Remark 1.1. The assumption “M is Li-bounded for each i”isnecessaryfor the condition of the equality. For counterexample, assume n =2andL¯ is induced from an arithmetically ample line bundle L on an integral model X of X.Let↵ : X0!Xbe the blowing-up of a closed point on ... martini abbigliamentoWebHodge bundles File (s) Name Griffiths_Completion.pdf Description Paper Size 659.98 KB Format Adobe PDF View/Download Downloads 72 Acquisition Date Mar 29, 2024 Views 353 Acquisition Date Mar 29, 2024 data link control framingWebdoes it follow that Lis semi-ample (ie. some positive tensor power is globally generated)? This always holds when Xis normal, so the interesting case is when pis the normalisation. 0.0 Definition. Let Lbe a nef line bundle on a complete algebraic space X. Two closed points x 1,x 2 ∈ Xare L-equivalent iff there is a connected closed curve x 1,x data link credit card feesWeb3 Modular forms and the Hodge bundle, the algebraic picture 5 4 De Rham cohomology and the Gauss-Manin connection 8 References 11 1 Elliptic curves By a curve over a eld k, we … data link coupler