Semistable Sheaves on Projective Varieties and Their Restriction to Curves.
Seshadri positive submanifolds of polarized manifolds
Let Y be a submanifold of dimension y of a polarized complex manifold (X, A) of dimension k ≥ 2, with 1 ≤ y ≤ k−1. We define and study two positivity conditions on Y in (X, A), called Seshadri A-bigness and (a stronger one) Seshadri A-ampleness. In this way we get a natural generalization of the theory initiated by Paoletti in [Paoletti R., Seshadri positive curves in a smooth projective 3-fold, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 1996, 6(4), 259–274] (which...
Shimuras Reziprozitätsgesetz für den Körper der arithmetischen elliptischen Funktionen beliebiger Stufe.
Siegel modular forms vanishing on the moduli space.
Signs in weight spectral sequences, monodromy-weight conjectures, log Hodge symmetry and degenerations of surfaces
Simple exponential estimate for the number of real zeros of complete abelian integrals
We show that for a generic polynomial and an arbitrary differential 1-form with polynomial coefficients of degree , the number of ovals of the foliation , which yield the zero value of the complete Abelian integral , grows at most as as , where depends only on . The main result of the paper is derived from the following more general theorem on bounds for isolated zeros occurring in polynomial envelopes of linear differential equations. Let , , be a fundamental system of real solutions...
Simultaneous resolution of rational singularities
Simultaneous Resolution of Threefold Double Points.
Singular open book structures from real mappings
We define open book structures with singular bindings. Starting with an extension of Milnor’s results on local fibrations for germs with nonisolated singularity, we find classes of genuine real analytic mappings which yield such open book structures.
Singular principal -bundles on nodal curves
In the present paper, we give a first general construction of compactified moduli spaces for semistable -bundles on an irreducible complex projective curve with exactly one node, where is a semisimple linear algebraic group over the complex numbers.
Singularités des espaces de modules de Hilbert, en les caractéristiques divisant le discriminant
Singularités rationelles et déformations.
Singularities of nets of quadrics
Singularity of the moduli space of stable bundles on surfaces
Some consequences of perversity of vanishing cycles
For a holomorphic function on a complex manifold, we show that the vanishing cohomology of lower degree at a point is determined by that for the points near it, using the perversity of the vanishing cycle complex. We calculate this order of vanishing explicitly in the case the hypersurface has simple normal crossings outside the point. We also give some applications to the size of Jordan blocks for monodromy.
Some invariant theory among quasi-projectives
Some moduli spaces of smooth complete intersections which are quasi-projective
For some values of the degrees of the equations, we show, using geometric invariant theory, that the coarse moduli space of smooth complete intersections in is quasi-projective.
Some nonreduced moduli of bundles and Donaldson invariants for Dolgachev surfaces.
Some polynomials on the blow-up of [...]
Some remarks concerning rank 2 bundles and Chow groups.