Blar i LUI - Institutt for grunnskole- og faglærerutdanning på forfatter "Hitching, George Harry"
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Brill–Noether loci on moduli spaces of symplectic bundles over curves
Hitching, George Harry; Bajravani, Ali (Collectanea Mathematica;, Journal article; Peer reviewed, 2020-11-20)The symplectic Brill–Noether locus Sk 2n,K associated to a curve C parametrises stable rank 2n bundles over C with at least k sections and which carry a nondegenerate skewsymmetric bilinear form with values in the canonical ... -
Counting maximal Lagrangian subbundles over an algebraic curve
Cheong, Daewoong; Choe, Insong; Hitching, George Harry (Journal of Geometry and Physics;Volume 167, September 2021, 104288, Peer reviewed; Journal article, 2021)Let C be a smooth projective curve and W a symplectic bundle over C. Let LQe(W) be the Lagrangian Quot scheme parametrizing Lagrangian subsheaves E ⊂ W of degree e. We give a closed formula for intersection numbers on ... -
Irreducibility of Lagrangian Quot schemes over an algebraic curve
Cheong, Daewoong; Choe, Insong; Hitching, George Harry (Mathematische Zeitschrift;, Peer reviewed; Journal article, 2021-08-03)Let C be a complex projective smooth curve and W a symplectic vector bundle of rank 2n over C. The Lagrangian Quot scheme LQ_{−e}(W) parameterizes subsheaves of rank n and degree −e which are isotropic with respect to the ... -
Isotropic Quot schemes of orthogonal bundles over a curve
Choe, Insong; Cheong, Daewoong; Hitching, George Harry (International Journal of Mathematics;, Peer reviewed; Journal article, 2021-05-19)We study the isotropic Quot schemes IQe(V ) parameterizing degree e isotropic subsheaves of maximal rank of an orthogonal bundle V over a curve. The scheme IQe(V ) contains a compactification of the space IQe◦(V ) of degree ... -
Low rank orthogonal bundles and quadric fibrations
Choe, Insong; Hitching, George Harry (Peer reviewed; Journal article, 2023)Let C be a curve and V → C an orthogonal vector bundle of rank r. For r ≤ 6, the structure of V can be described using ten- sor, symmetric and exterior products of bundles of lower rank, essentially due to the existence ... -
Non-defectivity of Grassmann bundles over a curve
Choe, Insong; Hitching, George Harry (Peer reviewed; Journal article, 2016-06-08)Let Gr(2, E) be the Grassmann bundle of two-planes associated to a general bundle E over a curve X. We prove that an embedding of Gr(2, E) by a certain twist of the relative Plücker map is not secant defective. This yields ... -
Nonemptiness and smoothness of twisted Brill-Noether loci
Hitching, George Harry; Hoff, Michael; Newstead, Peter E. (Annali di Matematica Pura ed Applicata; 200 (2021), Journal article; Peer reviewed, 2020-06-25)Let V be a vector bundle over a smooth curve C. In this paper, we study twisted Brill– Noether loci parametrising stable bundles E of rank n and degree e with the property that h0(C, V ⊗ E) ≥ k. We prove that, under ... -
Quot schemes, Segre invariants, and inflectional loci of scrolls over curves
Hitching, George Harry (Geometriae Dedicata;, Journal article; Peer reviewed, 2019-06-26)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 99K Pn in terms of Quot schemes of E. This gives a geometric ... -
A Riemann–Kempf singularity theorem for higher rank Brill-Noether loci
Hitching, George Harry (Bulletin of the London Mathematical Society;Volume 52, Issue 4, August 2020, Journal article; Peer reviewed, 2020-06-09)Given a vector bundle V over a curve X, we define and study a surjective rational map Hilbd(PV ) 99K Quot0,d(V ∗) generalising the natural map SymdX → Quot0,d(OX). We then give a generalisation of the geometric Riemann–Roch ... -
A stratification on the moduli spaces of symplectic and orthogonal bundles over a curve
Hitching, George Harry; Choe, Insong (International Journal of Mathematics;25(5), Journal article; Peer reviewed, 2014-05-22)A symplectic or orthogonal bundle V of rank 2n over a curve has an invariant t(V) which measures the maximal degree of its isotropic subbundles of rank n. This invariant t defines stratifications on moduli spaces of ... -
Tangent cones to generalised theta divisors and generic injectivity of the theta map
Hitching, George Harry; Hoff, Michael (Journal article; Peer reviewed, 2017)Let be a Petri general curve of genus and a general stable vector bundle of rank and slope over with . For , we show how the bundle can be recovered from the tangent cone to the generalised theta divisor at . We use this ... -
Theta divisors of stable vector bundles may be nonreduced
Hitching, George Harry; Pauly, Christian (Geometriae Dedicata;, Journal article; Peer reviewed, 2014-05-28)A generic strictly semistable bundle of degree zero over a curve X has a reducible theta divisor, given by the sum of the theta divisors of the stable summands of the associated graded bundle. The converse is not true: ...