Lefschetz hyperplane theorem information

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

Lefschetz pencil of hyperplane sections is a more subtle system than a Morse function because hyperplanes intersect each other). The Picard–Lefschetz...

collectively as Bertini's theorem. The topology of hyperplane sections is studied in the topic of the Lefschetz hyperplane theorem and its refinements. Because...

theorem (topology) Lefschetz hyperplane theorem (algebraic topology) Lefschetz theorem on (1,1)-classes (algebraic geometry) Lehmann–Scheffé theorem (statistics)...

non-singular projective surface, and let H be the divisor class on V of a hyperplane section of V in a given projective embedding. Then the intersection H...

{\displaystyle H^{1,1}(X)} given by the Lefschetz class [ L ] {\displaystyle [L]} . From the Lefschetz hyperplane theorem and Hodge duality, the rest of the...

inverse Parallelizable manifold Thom's and Bott's proofs of the Lefschetz hyperplane theorem Atiyah, Michael (2007). "Raoul Harry Bott. 24 September 1923...

\geq 2} (this is because of the Hurewicz homomorphism and the Lefschetz hyperplane theorem). In this case the local systems R q f ∗ ( Q _ X ) {\displaystyle...

using the definition of the Euler characteristic and using the Lefschetz hyperplane theorem. If X ⊂ P 3 {\displaystyle X\subset \mathbb {P} ^{3}} is a degree...

analogue of the Riemann hypothesis. It also led to the proof of Lefschetz hyperplane theorem and the old and new estimates of the classical exponential sums...

projective spaces Adequate equivalence relation Hilbert scheme Lefschetz hyperplane theorem Minimal model program Kollár & Moduli, Ch I. Shafarevich, Igor...

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

vanishing theorem Lefschetz hyperplane theorem: an ample divisor in a complex projective variety X is topologically similar to X. Hartshorne (1977), Theorem II...

axioms of a Weil theory is the so-called hard Lefschetz theorem (or axiom): Begin with a fixed smooth hyperplane section W = H ∩ X, where X is a given smooth...

René Thom, Frankel and Aldo Andreotti gave a new proof of the Lefschetz hyperplane theorem using Morse theory. The crux of the argument is the algebraic...

\mathbb {CP} ^{n+m}} are the intersection of hyperplane sections, we can use the Lefschetz hyperplane theorem to deduce that H j ( X ) = Z {\displaystyle...

has an associated long exact sequence in cohomology. From the Lefschetz hyperplane theorem there is only one interesting cohomology group of X {\displaystyle...

space of formal group laws. Lefschetz 1.  Solomon Lefschetz 2.  The Lefschetz fixed-point theorem says: given a finite simplicial complex K and its geometric...

projective space Plane at infinity, hyperplane at infinity Projective frame Projective transformation Fundamental theorem of projective geometry Duality (projective...

structure on H 3 ( X ) {\displaystyle H^{3}(X)} . Using the Lefschetz hyperplane theorem the only non-trivial cohomology group is H 3 ( X ) {\displaystyle...

analogues of the Lefschetz hyperplane theorems. In general such theorems state that homology or cohomology is supported on a hyperplane section of an algebraic...

equal. Subspace theorem Schmidt's subspace theorem shows that points of small height in projective space lie in a finite number of hyperplanes. A quantitative...

be the inclusion Z ⊂ K. Weak Lefschetz axiom: For any smooth hyperplane section j: W ⊂ X (i.e. W = X ∩ H, H some hyperplane in the ambient projective space)...