Non-defectivity of Grassmannian bundles over a curve

Choe, Insong; Hitching, George H.

doi:10.1142/s0129167x16400024

Cited by 3 publications

(3 citation statements)

References 12 publications

(28 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [LN83], the Segre invariants of rank two bundles are interpreted geometrically in terms of secant varieties to a projective model of the curve. This interpretation is generalised to higher rank and to symplectic and orthogonal bundles in [CH10,CH12,CH16] and elsewhere.…”

Section: Introductionmentioning

confidence: 87%

See 1 more Smart Citation

Quot schemes, Segre invariants, and inflectional loci of scrolls over curves

Hitching

2019

Geom Dedicata

Self Cite

View full text Add to dashboard Cite

Let E be a vector bundle over a smooth curve C, and S = PE the associated projective bundle. We describe the inflectional loci of certain projective models ψ : S P n in terms of Quot schemes of E. This gives a geometric characterisation of the Segre invariant s1(E), which leads to new geometric criteria for semistability and cohomological stability of bundles over C. We also use these ideas to show that for general enough S and ψ, the inflectional loci are all of the expected dimension. An auxiliary result, valid for a general subvariety of P n , is that under mild hypotheses, the inflectional loci associated to a projection from a general centre are of the expected dimension.

show abstract

Section: Introductionmentioning

confidence: 87%

“…This approach was utilised in [KS88] for E = O C = M , and in [CH12], [CH16] and elsewhere for bundles of higher rank. Generalising, we now use principal parts to describe Osc k (S, x) directly as a subspace of PH 1 (C, KM −1 ⊗ E) for all k ≥ 0.…”

Section: Osculating Spaces Via Principal Partsmentioning

confidence: 99%

Quot schemes, Segre invariants, and inflectional loci of scrolls over curves

Hitching

2019

Geom Dedicata

Self Cite

View full text Add to dashboard Cite

show abstract

“…When there are sections of both components defining subbundles of the same degree, IQ • e (V ) cannot be connected. (See [11,Theorem 5.3]. ) (ii) Any two isotropic subbundles defining sections of the same component of OG(n, V ) have degrees of the same parity (Theorem 2.13).…”

Section: Introductionmentioning

confidence: 99%

Isotropic Quot schemes of orthogonal bundles over a curve

Cheong¹,

Choe²,

Hitching³

2020

Preprint

Self Cite

View full text Add to dashboard Cite

We study the isotropic Quot schemes IQ e (V ) parameterizing degree e isotropic subsheaves of maximal rank of an orthogonal bundle V over a curve. The scheme IQ e (V ) contains a compactification of the space IQ • e (V ) of degree e maximal isotropic subbundles, but behaves quite differently from the classical Quot scheme, and the Lagrangian Quot scheme in [6]. We observe that for certain topological types of V , the scheme IQ e (V ) is empty for all e. In the remaining cases, for infinitely many e there are irreducible components of IQ e (V ) consisting entirely of nonsaturated subsheaves, and so IQ e (V ) is strictly larger than the closure of IQ • e (V ). As our main result, we prove that for any orthogonal bundle V and for e ≪ 0, the closure IQ • e (V ) of IQ • e (V ) is either empty or consists of one or two irreducible connected components, depending on deg(V ) and e. In so doing, we also characterize the nonsaturated part of IQ • e (V ) when V has even rank.

show abstract

Isotropic Quot schemes of orthogonal bundles over a curve

2021

View full text Add to dashboard Cite

We study the isotropic Quot schemes [Formula: see text] parametrizing degree [Formula: see text] isotropic subsheaves of maximal rank of an orthogonal bundle [Formula: see text] over a curve. The scheme [Formula: see text] contains a compactification of the space [Formula: see text] of degree [Formula: see text] maximal isotropic subbundles, but behaves quite differently from the classical Quot scheme, and the Lagrangian Quot scheme in [D. Cheong, I. Choe and G. H. Hitching, Irreducibility of Lagrangian Quot schemes over an algebraic curve, preprint (2019), arXiv:1804.00052, v2]. We observe that for certain topological types of [Formula: see text], the scheme [Formula: see text] is empty for all [Formula: see text]. In the remaining cases, for infinitely many [Formula: see text] there are irreducible components of [Formula: see text] consisting entirely of nonsaturated subsheaves, and so [Formula: see text] is strictly larger than the closure of [Formula: see text]. As our main result, we prove that for any orthogonal bundle [Formula: see text] and for [Formula: see text], the closure [Formula: see text] of [Formula: see text] is either empty or consists of one or two irreducible connected components, depending on [Formula: see text] and [Formula: see text]. In so doing, we also characterize the nonsaturated part of [Formula: see text] when [Formula: see text] has even rank.

show abstract

Non-defectivity of Grassmannian bundles over a curve

Cited by 3 publications

References 12 publications

Quot schemes, Segre invariants, and inflectional loci of scrolls over curves

Quot schemes, Segre invariants, and inflectional loci of scrolls over curves

Isotropic Quot schemes of orthogonal bundles over a curve

Isotropic Quot schemes of orthogonal bundles over a curve

Contact Info

Product

Resources

About