On moduli spaces of parabolic vector bundles of rank 2 over CP1

Biswas, Indranil; Holla, Yogish I.; Kimar, Chanchal

doi:10.1307/mmj/1281531467

Cited by 10 publications

(10 citation statements)

References 4 publications

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“…Notice that Corollary 1.6 is a classical result, originally due to Coble (see [DO88] and references therein). See also [BHK10] for a result related to Corollary 1.7, in terms of moduli spaces of rank 2 parabolic vector bundles on P 1 .…”

Section: Introductionmentioning

confidence: 99%

On the Fano variety of linear spaces contained in two odd-dimensional quadrics

Araujo

Casagrande

2017

Geom. Topol.

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In this paper we describe the geometry of the 2m-dimensional Fano manifold G parametrizing (m − 1)-planes in a smooth complete intersection Z of two quadric hypersurfaces in the complex projective space P 2m+2 , for m ≥ 1. We show that there are exactly 2 2m+2 distinct isomorphisms in codimension one between G and the blow-up of P 2m at 2m + 3 general points, parametrized by the 2 2m+2 distinct m-planes contained in Z, and describe these rational maps explicitly. We also describe the cones of nef, movable and effective divisors of G, as well as their dual cones of curves. Finally, we determine the automorphism group of G.These results generalize to arbitrary even dimension the classical description of quartic del Pezzo surfaces (m = 1).

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Section: Introductionmentioning

confidence: 99%

On the Fano variety of linear spaces contained in two odd-dimensional quadrics

Araujo

Casagrande

2017

Geom. Topol.

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“…For a generic choice of m 1 , there are two of these line subbundles passing through m 1 , thus defining generically two parabolic directions on the fiber of t 2 (see Proposition 3.3). Hence, the locus of strictly µ-semistable parabolic configurations is a curve of bidegree (2,2). Theorem 4.2 shows that this locus is exactly Γ.…”

Section: 1mentioning

confidence: 93%

“…Proof of Theorem B. Let G = PGL(2) × PGL (2). We have to show that there are one-to-one correspondences between the sets…”

Section: 1mentioning

confidence: 99%

Geometry of the moduli of parabolic bundles on elliptic curves

Vargas¹

2021

Trans. Amer. Math. Soc.

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The goal of this paper is the study of simple rank 2 parabolic vector bundles over a 2-punctured elliptic curve C. We show that the moduli space of these bundles is a non-separated gluing of two charts isomorphic to P 1 × P 1 . We also showcase a special curve Γ isomorphic to C embedded in this space, and this way we prove a Torelli theorem. This moduli space is related to the moduli space of semistable parabolic bundles over P 1 via a modular map which turns out to be the 2:1 cover ramified in Γ. We recover the geometry of del Pezzo surfaces of degree 4 and we reconstruct all their automorphisms via elementary transformations of parabolic vector bundles. IRMAR, Univ. Rennes

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“…Given weights, the moduli space of semistable points P w d (t) is a (separated but may be singular) projective variety; moreover, stable points are smooth (cf. [15], [5], [7], [14], [6] and [23]).…”

Section: And Only If It Is Stable For a Convenient Choice Of Weights Wmentioning

confidence: 99%

Lagrangian Fibrations in Duality on Moduli Spaces of Rank 2 Logarithmic Connections Over the Projective Line

Loray

Saito

2013

International Mathematics Research Notices

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We study the moduli space of logarithmic connections of rank 2 on P 1 C minus n points with fixed spectral data. There are two natural Lagrangian maps: one towards apparent singularities of the associated fuchsian scalar equation, and another one towards moduli of parabolic bundles. We show that these are transversal and dual to each other. In case n = 5, we recover the beautiful geometry of Del Pezzo surfaces of degree 4.

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On moduli spaces of parabolic vector bundles of rank 2 over CP1

Cited by 10 publications

References 4 publications

On the Fano variety of linear spaces contained in two odd-dimensional quadrics

On the Fano variety of linear spaces contained in two odd-dimensional quadrics

Geometry of the moduli of parabolic bundles on elliptic curves

Lagrangian Fibrations in Duality on Moduli Spaces of Rank 2 Logarithmic Connections Over the Projective Line

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