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Papers by Nadezda Timofeeva

Математический сборник, 2013

УДК 512.722+512.723 Н. В. Тимофеева О новой компактификации модулей векторных расслоений на повер... more УДК 512.722+512.723 Н. В. Тимофеева О новой компактификации модулей векторных расслоений на поверхности. V: Существование универсального семейства Исследуется существование универсального семейства/псевдосемейства допустимых стабильных пар над пространством модулей M , полученном в предыдущих работах. Библиография: 16 названий. Ключевые слова: пространство модулей, полустабильные когерентные пучки, алгебраическая поверхность, универсальное семейство, псевдосемейство.

Sbornik: Mathematics, 2009

A new compactification for the scheme of moduli for Gieseker-stable vector bundles with prescribe... more A new compactification for the scheme of moduli for Gieseker-stable vector bundles with prescribed Hilbert polynomial, on the smooth projective polarized surface (S, L), is constructed. We work over the field k =k of characteristic zero. Families of locally free sheaves on the surface S are completed with locally free sheaves on schemes which are modifications of S. Gieseker-Maruyama moduli space has a birational morphism onto the new moduli space. We propose the functor for families of pairs "polarized scheme-vector bundle" with moduli space of such type.

Математический сборник

Построены морфизмы между функтором модулей допустимых полустабильных пар и функтором модулей Гизе... more Построены морфизмы между функтором модулей допустимых полустабильных пар и функтором модулей Гизекера-Маруямы (полустабильных когерентных пучков без кручения) с тем же полиномом Гильберта на поверхности. Показано, что рассматриваемые функторы изоморфны. Таким образом, схема модулей полустабильных допустимых пар ((widetildeS,widetildeL),widetildeE)((\widetilde S, \widetilde L), \widetilde E)((widetildeS,widetildeL),widetildeE) изоморфна схеме модулей по Гизекеру-Маруяме. В рассмотрение включены все существующие компоненты функторов модулей и соответствующих схем модулей. Библиография: 16 названий.

Mathematical Notes

We prove that the varieties X d 1 d 2 of complete pairs of zero-dimensional subschemes of lengths... more We prove that the varieties X d 1 d 2 of complete pairs of zero-dimensional subschemes of lengths d 1 ≥ 2 , d 2 ≥ 4 on a smooth irreducible projective algebraic surface are singular.

We prove a theorem on how a conclusion on homological dimension of a family of coherent sheaves o... more We prove a theorem on how a conclusion on homological dimension of a family of coherent sheaves over a scheme can be done from homological dimension of the restriction of this family to the reduction of the base.

Math Notes Engl Tr, 2001

We construct a determinantal resolution of singularities for the universal subscheme in S × H d+1... more We construct a determinantal resolution of singularities for the universal subscheme in S × H d+1 and prove that it is isomorphic to the variety of total pairs S × H d .

A morphism of the reduced Gieseker -Maruyama moduli functor (of semistable coherent torsion-free ... more A morphism of the reduced Gieseker -Maruyama moduli functor (of semistable coherent torsion-free sheaves) to the reduced moduli functor of admissible semistable pairs with the same Hilbert polynomial, is constructed. It is shown that main components of reduced moduli scheme for semistable admissible pairs (( S, L), E) are isomorphic to main components of reduced Gieseker -Maruyama moduli scheme.

The construction for (possibly) nonreduced moduli of semistable admissible pairs is performed. We... more The construction for (possibly) nonreduced moduli of semistable admissible pairs is performed. We establish the connection or this moduli scheme with reduced moduli scheme done in the previous article and investigate when the nonreduced moduli scheme carries a universal family

A morphism of nonreduced Gieseker - Maruyama functor (of semistable coherent torsion-free sheaves... more A morphism of nonreduced Gieseker - Maruyama functor (of semistable coherent torsion-free sheaves) on a surface to the nonreduced functor of admissible semistable pairs with the same Hilbert polynomial, is constructed. This leads to the morphism of moduli schemes with possibly nonreduced scheme structures. As usually, we consider subfunctors corresponding to main components of moduli schemes.

The method involves description of algebras by generators and relations on input and returns simi... more The method involves description of algebras by generators and relations on input and returns similar description of the product algebra. It is "ready-to-eat" even for computer realization. The product algebra is well-defined: taking another descriptions of the same algebras leads to isomorphic product algebra. Also it is proven that the product algebra enjoys universal property, i.e. it is indeed fibred product. The input data is a triple of algebras and a pair of homomorphisms A1stackrelf1toA0stackrelf2leftarrowA_2A_1\stackrel{f_1}{\to}A_0 \stackrel{f_2}{\leftarrow}A_2A_1stackrelf_1toA_0stackrelf2leftarrowA2. Algebras and homomorphisms can be described in any fashion. We prove that for computing the fibred product it is enough to restrict to the case when fi,i=1,2,f_i,i=1,2,fi,i=1,2, are surjective and describe how to reduce to surjective case. Also the way to choose generators and relations for input algebras is considered.

The criterion for an affine primary algebra over the field to be integral, is proven. Using this ... more The criterion for an affine primary algebra over the field to be integral, is proven. Using this criterion we give a simple proof that Hilbert scheme of 0-dimensional subschemes of length lll of nonsingular ddd-dimensional algebraic variety is reduced for all ddd and lll.

St. Petersburg Mathematical Journal, 2014

The generalization of the well-known criterion for flatness of a projective morphism of Noetheria... more The generalization of the well-known criterion for flatness of a projective morphism of Noetherian schemes involving Hilbert polynomial, is given for the case of nonreduced base of the morphism.

The new compactification of moduli scheme of Gieseker-stable vector bundles with the given Hilber... more The new compactification of moduli scheme of Gieseker-stable vector bundles with the given Hilbert polynomial on a smooth projective polarized surface (S;H), over the field k = \bar k of zero characteristic, is constructed in previous papers of the author. Families of locally free sheaves on the surface S are completed by the locally free sheaves on the schemes which are certain modifications of S. We obtain the class of modified surfaces to appear in the construction. Keywords: moduli space, semistable coherent sheaves, blowup algebra, algebraic surface.

We construct a new compactiflcation of the moduli scheme of Gieseker-stable vector bun- dles havi... more We construct a new compactiflcation of the moduli scheme of Gieseker-stable vector bun- dles having prescribed Hilbert polynomial on the smooth projective polarized surface (S; H) deflned over a fleld k = „ k of zero characteristic. The families of locally free sheaves on the surface S are completed by locally free sheaves on the surfaces that are certain modiflcations of S. The new moduli space has a birational morphism onto Gieseker and Maruyama moduli space. We consider the case when the Gieseker and Maruyama space is the flne moduli space. Contents

$Research paper thumbnail of The homology groups of the variety of complete pairs $ X_{13}$ of zero-dimensional subschemes of lengths 1 and 3 of projective space$

Sbornik: Mathematics, 2000

Sbornik: Mathematics, 2008