Stability of symmetric powers of vector bundles of rank two with even degree on a curve

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This paper treats the strict semi-stability of the symmetric powers (SE)-E-k of a stable vector bundle E of rank 2 with even degree on a smooth projective curve C of genus g >= 2. The strict semi-stability of (SE)-E-2 is equivalent to the orthogonality of E or the existence of a bisection on the ruled surface P-C(E) whose self-intersection number is zero. A relation between the two interpretations is investigated in this paper through elementary transformations. This paper also gives a classification of E with strictly semi-stable (SE)-E-3. Moreover, it is shown that when (SE)-E-2 is stable, every symmetric power (SE)-E-k is stable for all but a finite number of E in the moduli of stable vector bundles of rank 2 with fixed determinant of even degree on C.
Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
Issue Date
2022-01
Language
English
Article Type
Article
Citation

INTERNATIONAL JOURNAL OF MATHEMATICS, v.33, no.01

ISSN
0129-167X
DOI
10.1142/S0129167X2250001X
URI
http://hdl.handle.net/10203/294808
Appears in Collection
RIMS Journal Papers
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