I am trying to understand a beautiful work of Pierre Schapira [5]. Notations and Conventions • For any set S we denote by IS the identity map S → S. For any subset A ⊂ S we denote by 1A the characteristic function of A. • In the sequel all manifolds will be assumed real analytic. A morphism of manifolds will be a real analytic map between two manifolds. Introduction Suppose we are given a simpl...

A normal complex algebraic variety X is called a symplectic variety (cf. [Be]) if its regular locus Xreg admits a holomorphic symplectic 2-form ω such that it extends to a holomorphic 2-form on a resolution f : X̃ → X. Affine symplectic varieties are constructed in various ways such as nilpotent orbit closures of a semisimple complex Lie algebra (cf. [CM]), Slodowy slices to nilpotent orbits (cf...

We construct two new versions of the c-map which allow us to obtain the target manifolds of hypermultiplets in Euclidean theories with rigid N = 2 supersymmetry. While the Minkowskian para-c-map is obtained by dimensional reduction of the Minkowskian vector multiplet lagrangian over time, the Euclidean para-c-map corresponds to the dimensional reduction of the Euclidean vector multiplet lagrang...

We prove that the Leray spectral sequence in rational cohomology for the quotient map U n,d → U n,d /G where U n,d is the affine variety of equations for smooth hypersurfaces of degree d in P n (C) and G is the general linear group, degenerates at E 2 .

We prove that the Leray spectral sequence in rational cohomology for the quotient map Un,d → Un,d/G where Un,d is the affine variety of equations for smooth hypersurfaces of degree d in P(C) and G is the general linear group, degenerates at E2. 2000 Math. Subj. Class. 14D20, 14L35, 14J70.

We prove that the Leray spectral sequence in rational cohomology for the quotient map U n,d → U n,d /G where U n,d is the affine variety of equations for smooth hypersurfaces of degree d in P n (C) and G is the general linear group, degenerates at E 2 .

We give a complete (global) characterization of $${\mathbb {C}}$$ -perverse sheaves on semi-abelian varieties in terms their cohomology jump loci. Our results generalize Schnell’s work perverse complex abelian varieties, as well Gabber–Loeser’s affine tori. apply our to the study loci smooth quasi-projective topology Albanese map, and context homological duality properties algebraic varieties.

Given an affine surjection of polytopes : P ! Q, the Generalized Baues Problem asks whether the poset of all proper polyhedral subdivisions of Q which are induced by the map has the homotopy type of a sphere. We extend earlier work of the last two authors on subdivisions of cyclic polytopes to give an affirmative answer to the problem for the natural surjections between cyclic polytopes : C(n; ...