In the spirit of a theorem of Wood, we give necessary and sufficient conditions for a family of germs of analytic hypersurfaces in a smooth projective toric variety to be interpolated by an algebraic hypersurface with a fixed class in the Picard group of .
In this note we review “quantum sheaf cohomology,” a deformation of sheaf cohomology that arises in a fashion closely akin to (and sometimes generalizing) ordinary quantum cohomology. Quantum sheaf cohomology arises in the study of (0,2) mirror symmetry, which we review. We then review standard topological field theories and the A/2, B/2 models, in which quantum sheaf cohomology arises, and outline basic definitions and computations. We then discuss (2,2) and (0,2) supersymmetric Landau-Ginzburg...
En esta nota se presenta en primer lugar una introducción autocontenida a la cohomología de álgebras de Lie, y en segundo lugar algunas de sus aplicaciones recientes en matemáticas y física.
We show that a subanalytic map-germ (Rⁿ,0) → (Rⁿ,0) which is arc-analytic and bi-Lipschitz has an arc-analytic inverse.
Si costruiscono famiglie di curve iperellittiche col —rango della varietà jacobiana uguale a zero. La costruzione sfrutta le proprietà elementari dell’operatore di Cartier e delle estensioni -cicliche dei corpi con la caratteristica maggiore di zero.
We give an example of a representation of the Kronecker quiver for which the closure of the corresponding orbit contains a singularity smoothly equivalent to the isolated singularity of two planes crossing at a point. Therefore this orbit closure is neither Cohen-Macaulay nor unibranch.
We construct analogs of the classical Δ-function for quotients of the upper half plane 𝓗 by certain arithmetic triangle groups Γ coming from quaternion division algebras B. We also establish a relative integrality result concerning modular functions of the form Δ(αz)/Δ(z) for α in B⁺. We give two explicit examples at the end.