Irreducibility of Lagrangian Quot schemes over an algebraic curve

被引：3

作者：

Cheong, Daewoong ^{[1
]}

Choe, Insong ^{[2
]}

Hitching, George H. ^{[3
]}

机构：

[1] Chungbuk Natl Univ, Dept Math, Chungdae Ro 1, Cheongju 28644, Chungbuk, South Korea

[2] Konkuk Univ, Dept Math, 1 Hwayang Dong, Seoul 143701, South Korea

[3] Oslo Metropolitan Univ, Postboks 4,St Olays Plass, N-0130 Oslo, Norway

来源：

MATHEMATISCHE ZEITSCHRIFT | 2022年 / 300卷 / 02期

关键词：

SYMPLECTIC BUNDLES; SUBBUNDLES;

D O I：

10.1007/s00209-021-02807-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 symplectic form. We prove that LQ(-e)(W) is irreducible and generically smooth of the expected dimension for all large e, and that a generic element is saturated and stable.

引用

页码：1265 / 1289

页数：25

共 6 条

[1] Isotropic Quot schemes of orthogonal bundles over a curve
Cheong, Daewoong
Choe, Insong
Hitching, George H.
INTERNATIONAL JOURNAL OF MATHEMATICS, 2021, 32 (08)
[2] Counting maximal Lagrangian subbundles over an algebraic curve
Cheong, Daewoong
Choe, Insong
Hitching, George H.
JOURNAL OF GEOMETRY AND PHYSICS, 2021, 167
[3] Quot schemes, Segre invariants, and inflectional loci of scrolls over curves
Hitching, George H.
GEOMETRIAE DEDICATA, 2020, 205 (01) : 1 - 19
[4] Moduli spaces of orthogonal and symplectic bundles over an algebraic curve
Serman, Olivier
COMPOSITIO MATHEMATICA, 2008, 144 (03) : 721 - 733
[5] Non-defectivity of Grassmannian bundles over a curve
Choe, Insong
Hitching, George H.
INTERNATIONAL JOURNAL OF MATHEMATICS, 2016, 27 (07)
[6] Counting maximal isotropic subbundles of orthogonal bundles over a curve
Cheong, Daewoong
Choe, Insong
Hitching, George H.
JOURNAL OF ALGEBRA, 2025, 663 : 727 - 764

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