DIGITAL.CSIChttps://digital.csic.esThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Tue, 21 May 2024 00:16:33 GMT2024-05-21T00:16:33Z5071Complex Lagrangians in a hyperKähler manifold and the relative Albanesehttp://hdl.handle.net/10261/235207Title: Complex Lagrangians in a hyperKähler manifold and the relative Albanese
Authors: Biswas, Indranil; Gomez, Tomas L.; Oliveira, Andre
Thu, 18 Mar 2021 10:10:03 GMThttp://hdl.handle.net/10261/2352072021-03-18T10:10:03ZOn vector bundles over moduli spaces trivial on hecke curveshttp://hdl.handle.net/10261/251077Title: On vector bundles over moduli spaces trivial on hecke curves
Authors: Biswas, Indranil; Gomez, Tomas L.
Abstract: Let MX(r, ¿) be the moduli space of stable vector bundles, on a smooth complex
projective curve X with genus(X) ¿ 3, of rank r and fixed determinant ¿ such that deg(¿)
is coprime to r. If E is a vector bundle MX(r, ¿) whose restriction to every Hecke curve in
MX(r, ¿) is trivial, we prove that E is trivial
Tue, 28 Sep 2021 08:40:11 GMThttp://hdl.handle.net/10261/2510772021-09-28T08:40:11ZModuli spaces for principal bundles in arbitrary characteristichttp://hdl.handle.net/10261/194881Title: Moduli spaces for principal bundles in arbitrary characteristic
Authors: Gomez, Tomas L.; Langer, A.; Schmitt, A. H. W.; Sols, I.
Abstract: In this article, we solve the problem of constructing moduli spaces of semistable principal bundles (and singular versions of them) over smooth projective varieties over algebraically closed ground fields of positive characteristic.
Tue, 19 Nov 2019 12:00:31 GMThttp://hdl.handle.net/10261/1948812019-11-19T12:00:31ZSemi-orthogonal decomposition of symmetric products of curves and canonical systemhttp://hdl.handle.net/10261/250242Title: Semi-orthogonal decomposition of symmetric products of curves and canonical system
Authors: Biswas, Indranil; Gomez, Tomas L.; Lee, Kyoung-Seog
Abstract: Let C be an irreducible smooth complex projective curve of genus
g ¿ 2 and Cd its d-fold symmetric product. In this paper, we study the question
of semi-orthogonal decompositions of the derived category of Cd. This entails
investigations of the canonical system on Cd, in particular its base locus.
Wed, 15 Sep 2021 09:10:12 GMThttp://hdl.handle.net/10261/2502422021-09-15T09:10:12ZStability of the Poincaré bundlehttp://hdl.handle.net/10261/251559Title: Stability of the Poincaré bundle
Authors: Biswas, Indranil; Gomez, Tomas L.; Hoffmann, Norbert
Abstract: Let X be an irreducible smooth projective curve, of genus at least two, over an algebraically closed field k. Let denote the moduli stack of principal G-bundles over X of fixed topological type d¿¿1(G), where G is any almost simple affine algebraic group over k. We prove that the universal bundle over is stable with respect to any polarization on . A similar result is proved for the Poincaré adjoint bundle over X×Md,rsG, where Md,rsG is the coarse moduli space of regularly stable principal G-bundles over X of fixed topological type d.
Mon, 04 Oct 2021 14:40:03 GMThttp://hdl.handle.net/10261/2515592021-10-04T14:40:03ZPoisson structure on the moduli spaces of sheaves of pure dimension one on a surfacehttp://hdl.handle.net/10261/230158Title: Poisson structure on the moduli spaces of sheaves of pure dimension one on a surface
Authors: Biswas, Indranil; Gomez, Tomas L.
Abstract: Let S be a smooth complex projective surface equipped with a Poisson structure s and also a polarization H. The moduli space M(S, P) of stable sheaves on S having a fixed Hilbert polynomial P of degree one has a natural Poisson structure given by s, Tyurin (Math USSR Izvest 33:139–177, 1989), Bottacin (Invent Math 121:421–436, 1995). We prove that the symplectic leaves of M(S, P) are the fibers of the natural map from it to the symmetric power of the effective divisor on S given by the singular locus of s.
Fri, 19 Feb 2021 10:40:53 GMThttp://hdl.handle.net/10261/2301582021-02-19T10:40:53ZAutomorphism group of the moduli space of parabolic bundles over a curvehttp://hdl.handle.net/10261/255443Title: Automorphism group of the moduli space of parabolic bundles over a curve
Authors: Alfaya, David; Gómez de Quiroga, Tomás Luis
Abstract: We find the automorphism group of the moduli space of parabolic bundles on a smooth curve (with fixed determinant and system of weights). This group is generated by: automorphisms of the marked curve, tensoring with a line bundle, taking the dual, and Hecke transforms (using the filtrations given by the parabolic structure). A Torelli theorem for parabolic bundles with arbitrary rank and generic weights is also obtained. These results are extended to the classification of birational equivalences which are defined over ¿big¿ open subsets (3-birational maps, i.e. birational maps giving an isomorphism between open subsets with complement of codimension at least 3).
Finally, an analysis of the stability chambers for the parabolic weights is performed in order to determine precisely when two moduli spaces of parabolic vector bundles with different parameters (curve, rank, determinant and weights) can be isomorphic.
Fri, 03 Dec 2021 12:30:12 GMThttp://hdl.handle.net/10261/2554432021-12-03T12:30:12Z