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  • Section 109. 19 (0E6N): The relative dualizing sheaf—The Stacks project
    109 19 The relative dualizing sheaf This section serves mainly to introduce notation in the case of families of curves Most of the work has already been done in the chapter on duality Let $f : X \to S$ be a family of curves
  • Dualizing sheaf - Wikipedia
    This is used in the construction of the Hodge bundle on the compactified moduli space of curves: it allows us to extend the relative canonical sheaf over the boundary which parametrizes nodal curves The Hodge bundle is then defined as the direct image of a relative dualizing sheaf
  • relative dualizing sheaf - Mathematics Stack Exchange
    Suppose we are given a projective smooth variety $X$ and a locally free sheaf $\mathcal {E}$ Now consider $\pi:\mathbb {P} (\mathcal {E})\rightarrow X$ One can define the relative dualizing sheaf as
  • Section 48. 28 (0E2S): Relative dualizing complexes—The Stacks project
    In this section we define relative dualizing complexes for morphisms which are flat and locally of finite presentation (but not necessarily quasi-separated or quasi-compact) between schemes (not necessarily locally Noetherian)
  • dualizing. dvi
    In this lecture, we introduce dualizing sheaves for projective schemes over a field, then use them to derive the Riemann-Roch theorem for curves Throughout, let k be a field (not necessarily algebraically closed), let j : X → P = PN
  • The direct image of the relative dualizing sheaf needs not be semiample . . .
    We provide details for the proof of Fujita's second theorem and prove that for a Kähler fibre space f: X → B over a smooth projective curve B, the direct image of the relative dualizing sheaf V: = f ⁎ ω X B is the direct sum of an ample and a unitary flat bundle
  • 216class5354. dvi - Stanford University
    We’ll prove the result in families (i e we’ll define a “relative dualizing sheaf” in good circumstances) This is useful in the theory of moduli of curves, and Gromov-Witten theory The existence of a dualizing sheaf will be straightforward to show — surprisingly so, at least to me
  • BASE CHANGE BEHAVIOR OF THE RELATIVE CANONICAL SHEAF RELATED TO HIGHER . . .
    This section contains a general overview on the base change properties of relative dualizing complexes and relative canonical sheaves For experts, some of the statements might be well known, still they are included here for completeness and easier reference
  • Relative dualizing sheaf (reference, behavior) - MathOverflow
    Kleiman, Steven L Relative duality for quasicoherent sheaves Compositio Math 41 (1980), no 1, 39–60 You'll find a detailed non-derived construction and a verification of the main properties of $\omega_ {X S}$ Thank you very much





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