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Новая бесконечная серия компонент модулей полустабильных пучков ранга 2 на P3 с особенностями смешанной размерности
Математический сборник. 2020. Т. 211. № 7. С. 72-92.
Иванов А. Н.
We construct a new infinite series of irreducible components of the Gieseker-Maruyama moduli scheme M(k), k≥3, of semistable rank-2 sheaves on P3 with Chern classes c1=0, c2=k and c3=0, whose general points are sheaves with singularities of mixed dimension. These sheaves are constructed by elementary transformations of stable and properly μ-semistable reflexive sheaves along disjoint unions of collections of points and smooth irreducible curves which are rational or complete intersection curves in P3. As a special member of this series, we obtain a new component of M(3).
Lavrov A., Tikhomirov A. S., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2017 Т. 476 № 6 С. 617-620
Мы описываем новую неприводимую компоненту схемы модулей Гизекера-Маруямы M(3) полустабильных когерентных пучков ранга 2 с классами Черна c_1=0, c_2=3, c_3=0 на P3, общая точка которой соответствует пучку с множеством особенностей, содержащим компоненты размерностей 0 и 1. Эти пучки получаются с помощью элементарных преобразований стабильных рефлексивных пучков ранга 2 с классами Черна c_1=0, c_2=2, c_3=2 вдоль ...
Added: June 19, 2017
Feigin B. L., Finkelberg M. V., Rybnikov L. G. et al., Selecta Mathematica, New Series 2011 Vol. 17 No. 2 P. 337-361
Laumon moduli spaces are certain smooth closures of the moduli spaces of maps from the projective line to the flag variety of GLn. We calculate the equivariant cohomology rings of the Laumon moduli spaces in terms of Gelfand-Tsetlin subalgebra of U(gln), and formulate a conjectural answer for the small quantum cohomology rings in terms of ...
Added: October 9, 2012
Gritsenko V., Nikulin V., Proceedings of the London Mathematical Society 2018 Vol. 116 No. 3 P. 485-533
We describe a new large class of Lorentzian Kac--Moody algebras. For all ranks, we classify 2-reflective hyperbolic lattices $S$ with the group of 2-reflections of finite volume and with a lattice Weyl vector. They define the corresponding hyperbolic Kac--Moody algebras of restricted arithmetic type which are graded by S. For most of them, we construct ...
Added: October 23, 2017
Gorinov A., / Cornell University. Series math "arxiv.org". 2014. No. 1402.5946.
We present a modification of the method of conical resolutions \cite{quintics,tom}. We apply our construction to compute the rational cohomology of the spaces of equations of nodal cubics in CP2, nodal quartics in CP2 and nodal cubics in CP3. In the last two cases we also compute the cohomology of the corresponding moduli spaces. ...
Added: February 26, 2014
Buryak A., Clader E., Tessler R., International Mathematics Research Notices 2022 Vol. 2022 No. 14 P. 10458-10532
We lay the foundation for a version of r-spin theory in genus zero for Riemann surfaces with boundary. In particular, we define the notion of r-spin disks, their moduli space, and the Witten bundle; we show that the moduli space is a compact smooth orientable orbifold with corners, and we prove that the Witten bundle is canonically ...
Added: October 29, 2021
Feigin B. L., Finkelberg M. V., Rybnikov L. G. et al., Selecta Mathematica, New Series 2011 Vol. 17 No. 3 P. 573-607
Laumon moduli spaces are certain smooth closures of the moduli spaces of maps from the projective line to the flag variety of GLn. We construct the action of the Yangian of sln in the cohomology of Laumon spaces by certain natural correspondences. We construct the action of the affine Yangian (two-parametric deformation of the universal ...
Added: October 9, 2012
Costa A., Gusein-Zade S., Natanzon S. M., Indiana University Mathematics Journal 2011 Vol. 60 No. 3 P. 985-995
Klein foams are analogues of Riemann and Klein surfaces with one-dimensional singularities. We prove that the field of dianalytic functions on a Klein foam Ω coincides with the field of dianalytic functions on a Klein surface K Ω We construct the moduli space of Klein foams, and we prove that the set of classes of ...
Added: November 24, 2012
Maxim Kazarian, Norbury P., International Mathematics Research Notices 2024 Vol. 2024 No. 3 P. 1825-1867
We construct an infinite collection of universal—independent of (g,n)—polynomials in the Miller–Morita–Mumford classes κm ∈ H2m(Mg,n, Q), defined over the moduli space of genus g stable curves with n labeled points. We conjecture vanishing of these polynomials in a range depending on g and n. ...
Added: February 19, 2024
Gritsenko V., Hulek K., / Cornell University. Series math "arxiv.org". 2015. No. 02723.
In this paper we consider moduli spaces of polarized and numerically polarized Enriques surfaces. The moduli spaces of numerically polarized Enriques surfaces can be described as open subsets of orthogonal modular varieties of dimension 10. One of the consequences of our description is that there are only finitely many birational equivalence classes of moduli spaces ...
Added: February 20, 2015
Verbitsky M., Duke Mathematical Journal 2013 Vol. 162 No. 15 (2013) P. 2929-2986
A mapping class group of an oriented manifold is a quotient of its diffeomorphism group by the isotopies. We compute a mapping class group of a hyperkähler manifold $M$, showing that it is commensurable to an arithmetic lattice in SO(3, b_2-3). A Teichmüller space of $M$ is a space of complex structures on $M$ up ...
Added: December 10, 2013
Natanzon S. M., Pratoussevitch A., Russian Mathematical Surveys 2016 Vol. 71 No. 2 P. 382-384
In this paper, we present all higher spinor structures on Klein surfaces. We present also topological invariants that describe the connected components of moduli of Klein surfaces with higher spinor structure. Each connected component is represented as a cell factorable by a discrete group . ...
Added: March 25, 2016
Finkelberg M. V., Rybnikov L. G., Algebraic Geometry 2014 Vol. 1 No. 2 P. 166-180
Drinfeld zastava is a certain closure of the moduli space of maps from the projective line to the Kashiwara flag scheme of an affine Lie algebra g^. In case g is the symplectic Lie algebra spN, we introduce an affine, reduced, irreducible, normal quiver variety Z which maps to the zastava space isomorphically in characteristic 0. The natural Poisson structure on ...
Added: October 25, 2013
Poberezhny V. A., / ИТЭФ. Series "Препринты ИТЭФ". 2013. No. 52/13.
We give an w\explicit example of non-regular behaviour of fuchsian systems moduli space in the case of resonant singular points. Tha set of systems with same singularities, asymptotics and monodromy but still not globally equivalent is constructed. ...
Added: March 31, 2014
Kochetkov Y., / Cornell University Library. 2013. No. 1301.6059.
We consider the space $\mathcal{M}_{2,1}$ --- the open moduli space of complex curves of genus 2 with one marked point. Using language of chord diagrams we describe the cell structure of $\mathcal{M}_{2,1}$ and cell adjacency. This allows one to construct matrices of boundary operators and compute Betty numbers of $\mathcal{M}_{2,1}$ over $\mathbb{Q}$. ...
Added: February 24, 2013
Bolbachan V., Geometriae Dedicata 2021 No. 215 P. 443-455
To any cubic surface, one can associate a cubic threefold given by a triple cover of P3P3 branched in this cubic surface. D. Allcock, J. Carlson, and D. Toledo used this construction to define the period map for cubic surfaces. It is interesting to calculate this map for some specific cubic surfaces. In this paper, we have ...
Added: May 28, 2022
Kazaryan M., Lando S., Moscow Mathematical Journal 2012 Vol. 12 No. 2 P. 397-411
Let Mg;n denote the moduli space of genus g stable algebraic curves with n marked points. It carries the Mumford cohomology classes ki. A homology class in H*(Mg;n) is said to be k-zero if the integral of any monomial in the k-classes vanishes on it. We show that any k-zero class implies a partial differential ...
Added: May 24, 2012
Boston : International Press of Boston Inc, 2013
The Handbook of Moduli, comprising three volumes, offers a multi-faceted survey of a rapidly developing subject aimed not just at specialists but at a broad community of producers of algebraic geometry, and even at some consumers from cognate areas. The thirty-five articles in the Handbook, written by fifty leading experts, cover nearly the entire range of the field. They ...
Added: February 27, 2015
Buryak A., Tessler R., Communications in Mathematical Physics 2017 Vol. 353 No. 3 P. 1299-1328
In a recent work, R. Pandharipande, J. P. Solomon and the second author have initiated a study of the intersection theory on the moduli space of Riemann surfaces with boundary. They conjectured that the generating series of the intersection numbers satisfies the open KdV equations. In this paper we prove this conjecture. Our proof goes ...
Added: September 27, 2020
Kazaryan M., Lando S., Prasolov V., Switzerland : Springer, 2018
This book offers a concise yet thorough introduction to the notion of moduli spaces of complex algebraic curves. Over the last few decades, this notion has become central not only in algebraic geometry, but in mathematical physics, including string theory, as well.
The book begins by studying individual smooth algebraic curves, including the most beautiful ones, ...
Added: November 19, 2018
Kochetkov Y., Фундаментальная и прикладная математика 2014 Т. 19 № 1 С. 45-63
Мы рассматриваем открытое пространство модулей $\mathcal{M}_{2,1}$ комплексных кривых рода 2 с одной отмеченной точкой. На языке хордовых диаграмм мы описываем клеточную структуру пространства $\mathcal{M}_{2,1}$ и структуру примыкания клеток. Это позволяет нам построить матрицы граничных операторов и найти числа Бетти пространства $\mathcal{M}_{2,1}$ над Q. ...
Added: November 11, 2014
Gritsenko V., / Cornell University. Series math "arxiv.org". 2010. No. 3753.
We prove that the existence of a strongly reflective modular form of a large weight implies that the Kodaira dimension of the corresponding modular variety is negative or, in some special case, it is equal to zero. Using the Jacobi lifting we construct three towers of strongly reflective modular forms with the simplest possible divisor. ...
Added: March 3, 2015
Gorsky E., Advances in Mathematics 2014 Vol. 250 P. 588-595
We derive a formula for the Sn-equivariant Euler characteristic of the moduli space Mg,n of genus g curves with n marked points. ...
Added: December 9, 2014
Gritsenko V., Hulek K., Sankaran G., Compositio Mathematica 2010 Vol. 146 No. 2 P. 404-434
We study the moduli spaces of polarised irreducible symplectic manifolds. By a comparison with locally symmetric varieties of orthogonal type of dimension 20, we show that the moduli space of 2d polarised (split type) symplectic manifolds which are deformation equivalent to degree 2 Hilbert schemes of a K3 surface is of general type if d ...
Added: March 3, 2015
Springer, 2020
This volume collects contributions from speakers at the INdAM Workshop “Birational Geometry and Moduli Spaces”, which was held in Rome on 11–15 June 2018. The workshop was devoted to the interplay between birational geometry and moduli spaces and the contributions of the volume reflect the same idea, focusing on both these areas and their interaction. ...
Added: August 13, 2020