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Sections du fibré déterminant sur l'espace de modules des faisceaux semi-stables de rang 2 sur le plan projectif

Gentiana Danila (2000)

Annales de l'institut Fourier

La conjecture de “dualité étrange” de Le Potier donne un isomorphisme entre l’espace des sections du fibré déterminant sur deux espaces de modules différents de faisceaux semi-stables sur le plan projectif ℙ 2 . Si on considère deux classes orthogonales c , u dans l’algèbre de Grothendieck K ( ℙ 2 ) telles que c est de rang strictement positif et u est de rang zéro, on note M c et M u les espaces de modules de faisceaux semi-stables de classe c , respectivement u , sur ℙ 2 . Il existe sur M c (resp. M u ) un fibré déterminant...

Semistability of Frobenius direct images over curves

Vikram B. Mehta, Christian Pauly (2007)

Bulletin de la Société Mathématique de France

Let X be a smooth projective curve of genus g ≥ 2 defined over an algebraically closed field k of characteristic p > 0 . Given a semistable vector bundle  E over X , we show that its direct image F * E under the Frobenius map F of X is again semistable. We deduce a numerical characterization of the stable rank- p vector bundles  F * L , where L is a line bundle over X .

Seshadri positive submanifolds of polarized manifolds

Lucian Bădescu, Mauro Beltrametti (2013)

Open Mathematics

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...

Simple exponential estimate for the number of real zeros of complete abelian integrals

Dmitri Novikov, Sergei Yakovenko (1995)

Annales de l'institut Fourier

We show that for a generic polynomial H = H ( x , y ) and an arbitrary differential 1-form ω = P ( x , y ) d x + Q ( x , y ) d y with polynomial coefficients of degree ≤ d , the number of ovals of the foliation H = const , which yield the zero value of the complete Abelian integral I ( t ) = ∮ H = t ω , grows at most as exp O H ( d ) as d → ∞ , where O H ( d ) depends only on H . 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 f 1 ( t ) , ⋯ , f n ( t ) , t ∈ K ⋐ ℝ , be a fundamental system of real solutions...

Singular open book structures from real mappings

Raimundo Araújo dos Santos, Ying Chen, Mihai Tibăr (2013)

Open Mathematics

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 G -bundles on nodal curves

Alexander Schmitt (2005)

Journal of the European Mathematical Society

In the present paper, we give a first general construction of compactified moduli spaces for semistable G -bundles on an irreducible complex projective curve X with exactly one node, where G is a semisimple linear algebraic group over the complex numbers.

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