In mathematics, a Lefschetz pencil is a construction in algebraic geometry considered by Solomon Lefschetz, used to analyse the algebraic topology of an algebraic variety V.
In mathematics, a Lefschetzpencil is a construction in algebraic geometry considered by Solomon Lefschetz, used to analyse the algebraic topology of an...
Lefschetzpencil of hyperplane sections is a more subtle system than a Morse function because hyperplanes intersect each other). The Picard–Lefschetz...
singularities. The theory of monodromy of Lefschetzpencils, introduced for complex varieties (and ordinary cohomology) by Lefschetz (1924), and extended by Grothendieck...
zero for k ≤ n − 1 {\displaystyle k\leq n-1} . Solomon Lefschetz used his idea of a Lefschetzpencil to prove the theorem. Rather than considering the hyperplane...
degenerate. Another useful class of examples of projective morphisms are LefschetzPencils: they are projective morphisms π : X → P k 1 = Proj ( k [ s , t...
supports of all the effective divisors in the system. Consider the Lefschetzpencil p : X → P 1 {\displaystyle p:{\mathfrak {X}}\to \mathbb {P} ^{1}} given...
at a given point. (As in the case when this procedure constructs a Lefschetzpencil.) In fact, it is possible for a bundle to have no non-zero global sections...
instanton invariants). Any compact symplectic manifold admits a symplectic Lefschetzpencil (Donaldson 1999). Donaldson's recent work centers on a problem in complex...
understanding varieties of higher dimension. A basic tool for that is the Lefschetzpencil. Hartshorne, Robin (1977), Algebraic Geometry, Graduate Texts in Mathematics...
Michael Artin (étale cohomology), Nick Katz (monodromy theory, and Lefschetzpencils). Jean Giraud worked out torsor theory extensions of nonabelian cohomology...
tangent to C. (Salmon 1879, p.96) pencil A 1-dimensional linear system. See pencil (mathematics) and Lefschetzpencil. pentad A set of 5 points pentahedron...
details, see the main article. Global proj can be used to construct Lefschetzpencils. For example, let X = P s , t 1 {\displaystyle X=\mathbb {P} _{s,t}^{1}}...
theorem. Von Neumann's model of an expanding economy considered the matrix pencil A − λB with nonnegative matrices A and B; von Neumann sought probability...
resolution of the Shafarevich-Tate conjecture for elliptic K3 surfaces and the pencil of elliptic curves over finite fields. He contributed to the theory of surface...
Institute for Advanced Study at Princeton where he worked with Solomon Lefschetz. On his return to England in 1936, Pedoe was appointed as an assistant...
on removable singularities, showing that any isolated singularity of a pencil of minimal surfaces can be removed; he spoke on this result at the 1950...
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