PulseExploreJournal ClubDebatesTrendingResearchersJournals
Instagram
HomeExploreJournal ClubTrending
Synapse
⌘+K
Synapse
April 26, 20260 citationsOpen Access

Generalized algebraic Morse inequalities and Hasse-Schmidt jet differentials

View Full Paper
BCBenoît Cadorel

Key Points

  • To provide a fully algebraic proof of Demailly's theorem about Green-Griffiths jet differentials and introduce a new version of Morse inequalities.
  • Introduced a new algebraic version of Morse inequalities applicable to positive characteristic.
  • Provided a proof of the existence of Green-Griffiths jet differentials in complex projective manifolds.
  • Applied findings to smooth projective varieties over arbitrary algebraically closed fields.
  • Demonstrated the existence of many Green-Griffiths jet differentials on complex projective manifolds of general type.
  • Presented new Morse inequalities that apply in positive characteristic contexts.
  • Established the existence of Hasse-Schmidt jet differentials for smooth projective varieties.

Abstract

This is a remastered and expanded version of a an earlier preprint of the author, in which we give a fully algebraic proof of an important theorem of Demailly, stating the existence of many Green-Griffiths jet differentials on a complex projective manifold of general type. To this end, we introduce a new algebraic version of the Morse inequalities, which we use in our proof as an algebraic counterpart to Demailly's and Bonavero's holomorphic Morse inequalities. This new version also applies to positive characteristic, giving the existence of Hasse-Schmidt jet differentials for a smooth projective variety of general type over an arbitrary algebraically closed field.

Ask AI
Helpful
Bookmark
Share
View Full Paper

Cite This Study

Benoît Cadorel (2026) studied this question.

synapsesocial.com/papers/69edaa9b4a46254e215b3198https://doi.org/10.48550/arxiv.2604.19207
Ask AI
Helpful
Bookmark
Share
View Full Paper

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Algebraic Morse theory via Homological Perturbation Lemma with two applications2024
  2. 2Invariant Jet Differentials and Asymptotic Serre Duality2025
  3. 3Geometric Implementation of Morse Theory Derived from Hecke Algebras in Ring Spaces2026
  4. 4Morse homology for a class of elliptic partial differential equations2025
  5. 5Symplectic Morse theory and Witten deformation2026 · 1 citations