Mumford-Tate groups of mixed Hodge structures and the theorem of the fixed part
Naive boundary strata and nilpotent orbits
We give a Hodge-theoretic parametrization of certain real Lie group orbits in the compact dual of a Mumford-Tate domain, and characterize the orbits which contain a naive limit Hodge filtration. A series of examples are worked out for the groups , , and .
Natural -constellation families.
Nets of Quadrics and Vector Bundles on a Double Plane.
Nichtsepariertheit instabiler Rang-2-Vektorbündel auf P2.
Nilpotent connections and the monodromy theorem : applications of a result of Turrittin
Nodal Cubic Surfaces and the Rationality of the Moduli Space of Curves of Genus Two.
Noether-Lefschetz, space curves and mathematical instantons.
Noncommutative compact manifolds constructed from quivers.
Non-commutative Hodge structures
This article gives a survey of recent results on a generalization of the notion of a Hodge structure. The main example is related to the Fourier-Laplace transform of a variation of polarizable Hodge structure on the punctured affine line, like the Gauss-Manin systems of a proper or tame algebraic function on a smooth quasi-projective variety. Variations of non-commutative Hodge structures often occur on the tangent bundle of Frobenius manifolds, giving rise to a tt* geometry.
Nonflat deformations of modules and isolated singularities.
Non-simple semistable vector bundles over a curve.
Non-smoothable varieties.
Normal degenerations of the complex projective plane.
Normal projective degenerations of rational and ruled surfaces.
Normalization theorems for certain modular discriminantal loci
Numerically trivial foliations
Given a positive singular hermitian metric of a pseudoeffective line bundle on a complex Kähler manifold, a singular foliation is constructed satisfying certain analytic analogues of numerical conditions. This foliation refines Tsuji’s numerically trivial fibration and the Iitaka fibration. Using almost positive singular hermitian metrics with analytic singularities on a pseudo-effective line bundle , a foliation is constructed refining the nef fibration. If the singularities of the foliation are...
Obstructions to deforming curves on a -fold, II: Deformations of degenerate curves on a del Pezzo -fold
We study the Hilbert scheme of smooth connected curves on a smooth del Pezzo -fold . We prove that any degenerate curve , i.e. any curve contained in a smooth hyperplane section of , does not deform to a non-degenerate curve if the following two conditions are satisfied: (i) and (ii) for every line on such that , the normal bundle is trivial (i.e. ). As a consequence, we prove an analogue (for ) of a conjecture of J. O. Kleppe, which is concerned with non-reduced components...
On a cell decomposition of the Hilbert scheme of points in the plane.
On a conjecture of H. Rauch on theta constants and Riemann surfaces with many automorphisms.