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chern.lib: a library for symbolic computations with Chern classes Iena, Oleksandr Software (2016) A basic toolbox for symbolic computations with Chern classes for computer algebra system Singular. The Aluffi's algorithms for computation of characteristic classes of algebraic varieties (Segre, Fulton ... [more ▼] A basic toolbox for symbolic computations with Chern classes for computer algebra system Singular. The Aluffi's algorithms for computation of characteristic classes of algebraic varieties (Segre, Fulton, Chern-Schwartz-MacPherson classes) are implemented as well. [less ▲] Detailed reference viewed: 129 (48 UL)On the singular sheaves in the fine Simpson moduli spaces of 1-dimensional sheaves Iena, Oleksandr ; Leytem, Alain in Canadian Mathematical Bulletin (2016) In the Simpson moduli space $M$ of semi-stable sheaves with Hilbert polynomial $dm-1$ on a projective plane we study the closed subvariety $M'$ of sheaves that are not locally free on their support. We ... [more ▼] In the Simpson moduli space $M$ of semi-stable sheaves with Hilbert polynomial $dm-1$ on a projective plane we study the closed subvariety $M'$ of sheaves that are not locally free on their support. We show that for $d\ge 4$ it is a singular subvariety of codimension $2$ in $M$. The blow up of $M$ along $M'$ is interpreted as a (partial) modification of $M\setminus M'$ by line bundles (on support). [less ▲] Detailed reference viewed: 99 (27 UL)goettsche.lib: a Singular library implementing the Göttsche's formula Iena, Oleksandr Software (2016) This is a library for the computer algebra system Singular. The Göttsche's formula for the Betti numbers of Hilbert schemes of points on a surface is implemented. An implementation of the Macdonald's ... [more ▼] This is a library for the computer algebra system Singular. The Göttsche's formula for the Betti numbers of Hilbert schemes of points on a surface is implemented. An implementation of the Macdonald's formula for the Betti numbers of symmetric products is provided as well. [less ▲] Detailed reference viewed: 57 (5 UL)On different approaches to compute the Chern classes of a tensor product of two vector bundles Iena, Oleksandr E-print/Working paper (2016) We compare four different approaches to compute the Chern classes of a tensor product of two vector bundles in terms of the Chern classes of the factors. Detailed reference viewed: 55 (4 UL)On 1-dimensional sheaves on projective plane Iena, Oleksandr Presentation (2016, January) Let M be the Simpson moduli space of semistable sheaves on the projective plane with fixed linear Hilbert polynomial P(m)=dm+c. A generic sheaf in M is a vector bundle on its Fitting support, which is a ... [more ▼] Let M be the Simpson moduli space of semistable sheaves on the projective plane with fixed linear Hilbert polynomial P(m)=dm+c. A generic sheaf in M is a vector bundle on its Fitting support, which is a planar projective curve of degree d. The sheaves that are not vector bundles on their support constitute a closed subvariety M' in M. We study the geometry of M' in the case of Hilbert polynomials dm-1 (for d bigger than 3) and demonstrate that M' is a singular variety of codimension 2 in M. We speculate on how the question we study is related to recompactifying of the Simpson moduli spaces by vector bundles. [less ▲] Detailed reference viewed: 82 (13 UL)A global description of the fine Simpson moduli space of 1-dimensional sheaves supported on plane quartics Iena, Oleksandr E-print/Working paper (2016) A global description of the fine Simpson moduli spaces of 1-dimensional sheaves supported on plane quartics is given: we describe the gluing of the Brill-Noether loci described by Drézet and Maican and ... [more ▼] A global description of the fine Simpson moduli spaces of 1-dimensional sheaves supported on plane quartics is given: we describe the gluing of the Brill-Noether loci described by Drézet and Maican and show that the Simpson moduli space M=M_{4m±1}(P_2) is a blow-down of a blow-up of a projective bundle over a smooth moduli space of Kronecker modules. An easy computation of the Poincaré polynomial of M is presented. [less ▲] Detailed reference viewed: 50 (17 UL)On the singular 1-dimensional planar sheaves supported on quartics Iena, Oleksandr in Rendiconti dell'Istituto di Matematica dell'Università di Trieste (2016) Detailed reference viewed: 17 (0 UL)Riemann Surfaces. Lecture notes. Winter semester 2015/2016. Iena, Oleksandr Learning material (2015) These are the lecture notes for the course 'Riemann surfaces' (14 Lectures, 90 minutes each). The lectures are provided with exercises. Detailed reference viewed: 63 (9 UL)On the singular sheaves in the fine Simpson moduli spaces of 1-dimensional sheaves supported on plane quartics Iena, Oleksandr in Rendiconti dell'Istituto di Matematica dell'Università di Trieste (2015) In the case of the fine Simpson moduli spaces of 1-dimensional sheaves supported on plane quartics, the subvariety of sheaves that are not locally free on their support is connected, singular, and has ... [more ▼] In the case of the fine Simpson moduli spaces of 1-dimensional sheaves supported on plane quartics, the subvariety of sheaves that are not locally free on their support is connected, singular, and has codimension 2. [less ▲] Detailed reference viewed: 57 (17 UL)A global description of the fine Simpson moduli space of 1-dimensional sheaves supported on plane quartics Iena, Oleksandr Poster (2015, September) We give a global description of the fine Simpson moduli spaces of 1-dimensional sheaves supported on plane quartics. Detailed reference viewed: 38 (10 UL)Universal Plane Curve and Moduli Spaces of 1-dimensional Coherent Sheaves Iena, Oleksandr in Communications in Algebra (2015), 43(2), 812-828 We show that the universal plane curve M of fixed degree d > 2 can be seen as a closed subvariety in a certain Simpson moduli space of 1-dimensional sheaves on a projective plane contained in the stable ... [more ▼] We show that the universal plane curve M of fixed degree d > 2 can be seen as a closed subvariety in a certain Simpson moduli space of 1-dimensional sheaves on a projective plane contained in the stable locus. The universal singular locus coincides with the subvariety of M consisting of sheaves that are not locally free on their support. It turns out that the blow up of M along M' may be naturally seen as a compactification of M_B = M\M' by vector bundles (on support). [less ▲] Detailed reference viewed: 60 (11 UL)On symbolic computations with Chern classes: remarks on the library chern.lib for Singular Iena, Oleksandr E-print/Working paper (2015) We provide an informal overview of the algorithms used for computing with Chern classes in the library chern.lib for the computer algebra system Singular. Detailed reference viewed: 89 (19 UL)lrcalc.lib: a Singular interface to the Littlewood-Richardson Calculator by Anders Buch Iena, Oleksandr Software (2015) This library for the computer algebra system Singular is an interface for the Littlewood-Richardson Calculator by Anders Buch. Detailed reference viewed: 77 (8 UL)Universal plane curve and moduli spaces of 1-dimensional coherent sheaves Iena, Oleksandr E-print/Working paper (2014) We show that the universal plane curve M of fixed degree d > 2 can be seen as a closed subvariety in a certain Simpson moduli space of 1-dimensional sheaves on a projective plane contained in the stable ... [more ▼] We show that the universal plane curve M of fixed degree d > 2 can be seen as a closed subvariety in a certain Simpson moduli space of 1-dimensional sheaves on a projective plane contained in the stable locus. The universal singular locus coincides with the subvariety of M consisting of sheaves that are not locally free on their support. It turns out that the blow up of M along M' may be naturally seen as a compactification of M_B = M\M' by vector bundles (on support). [less ▲] Detailed reference viewed: 53 (4 UL)Riemann Surfaces. Lecture notes. Winter semester 2014/2015. Iena, Oleksandr Learning material (2014) This is a preliminary version of lecture notes for the course 'Riemann surfaces' (14 Lectures, 90 minutes each). The lectures are provided with exercises. Detailed reference viewed: 80 (35 UL)Riemann Surfaces. Lecture notes. Winter semester 2013/2014. Iena, Oleksandr Learning material (2013) This is a preliminary version of lecture notes for the course 'Riemann surfaces' (14 Lectures, 90 minutes each). Detailed reference viewed: 53 (18 UL)Modifications of the Simpson moduli spaces of 1-dimensional sheaves on a projective plane by vector bundles Iena, Oleksandr Poster (2013, June) We study how to modify the Simpson moduli spaces of 1-dimensional coherent sheaves on a projective plane in order to obtain a space of vector bundles on curves. Detailed reference viewed: 22 (1 UL)Universal plane curves and Simpson moduli spaces of 1-dimensional sheaves Iena, Oleksandr Poster (2012, June) We show that the universal plane curve M of fixed degree d > 2 can be seen as a closed subvariety in a certain Simpson moduli space of 1-dimensional sheaves on a projective plane contained in the stable ... [more ▼] We show that the universal plane curve M of fixed degree d > 2 can be seen as a closed subvariety in a certain Simpson moduli space of 1-dimensional sheaves on a projective plane contained in the stable locus. The universal singular locus coincides with the subvariety of M consisting of sheaves that are not locally free on their support. It turns out that the blow up of M along M' may be naturally seen as a compactification of M_B = M\M' by vector bundles (on support). [less ▲] Detailed reference viewed: 30 (3 UL)Vector Bundles on Elliptic Curves and Factors of Automorphy Iena, Oleksandr in Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics (2011), 43 We translate Atiyah’s results on classification of vector bundles on elliptic curves to the language of factors of automorphy. Detailed reference viewed: 45 (5 UL) |
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