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specifically in algebraic geometry and algebraic topology, the Lefschetz hyperplane theorem is a precise statement of certain relations between the shape...

and MacPherson. The first case of the decomposition theorem arises via the hard Lefschetz theorem which gives isomorphisms, for a smooth proper map f...

manifolds, that of satisfying the conclusion of the Hard Lefschetz theorem. More precisely, the strong Lefschetz property asks that for k ∈ { 1 , … , n } {\displaystyle...

such as the Lefschetz hyperplane theorem, the hard Lefschetz theorem, the Hodge-Riemann bilinear relations, and the Hodge index theorem. They are also...

Grothendieck's standard conjectures remain open (except for the hard Lefschetz theorem, which was proved by Deligne by extending his work on the Weil conjectures)...

Nakano vanishing theorems, the Lefschetz hyperplane theorem, Hard Lefschetz theorem, Hodge-Riemann bilinear relations, and Hodge index theorem. On a Riemannian...

building on Hodge theory. The results include the Lefschetz hyperplane theorem, the hard Lefschetz theorem, and the Hodge-Riemann bilinear relations. Many...

conjecture for higher codimensional subvarieties. By the Hard Lefschetz theorem, one can prove: Theorem. If for some p < n 2 {\displaystyle p<{\frac {n}{2}}}...

This states a theorem calculating the Lefschetz number of an endomorphism of an elliptic complex. Atiyah, M. F.; Bott, R. (1967), "A Lefschetz Fixed Point...

as occurring 'in nature'. The decomposition theorem, a far-reaching extension of the hard Lefschetz theorem decomposition, requires the usage of perverse...

not listed. One of the axioms of a Weil theory is the so-called hard Lefschetz theorem (or axiom): Begin with a fixed smooth hyperplane section W = H ∩...

doi:10.1016/0095-8956(74)90071-9. ISSN 0095-8956. Huh, June. "Hard Lefschetz theorem and Hodge-Riemann relations for combinatorial geometries" (PDF)...

was 36 years old and Lefschetz was 73 years old), Peixoto and Lefschetz became good friends. Once, while talking with Lefschetz, Peixoto commented that...

"Combinatorial Lefschetz theorems beyond positivity". arXiv:1812.10454v3 [math.CO]. Karu, Kalle (2004-08-01). "Hard Lefschetz theorem for nonrational...

(eds.). Algebraic geometry and topology. A symposium in honor of S. Lefschetz. Princeton Mathematical Series. Vol. 12. Princeton, NJ: Princeton University...

such as the Riemann hypothesis (still a conjecture) or Fermat's Last Theorem (a conjecture until proven in 1995 by Andrew Wiles), have shaped much of...

his work in developing K-theory, a generalized Lefschetz fixed-point theorem and the Atiyah–Singer theorem, for which he also won the Abel Prize jointly...

However, the chairman of the mathematics department at Princeton, Solomon Lefschetz, offered him the John S. Kennedy fellowship, convincing Nash that Princeton...

cohérents et théorèmes de Lefschetz locaux et globaux, 1961–1962 (Local cohomology of coherent sheaves and global and local Lefschetz theorems), North Holland...

the hard stability theorem asserts that J {\displaystyle J} is Lipschitz continuous. Bottleneck distance is widely used in TDA. The isometry theorem asserts...