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On the Aut ( A 2 ) ‐action on G‐semistable locally free sheaves on P 2
Author(s) -
Miesener Michael
Publication year - 2013
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201100158
Subject(s) - mathematics , moduli space , lemma (botany) , divisor (algebraic geometry) , rank (graph theory) , pure mathematics , action (physics) , combinatorics , botany , physics , poaceae , quantum mechanics , biology
We show that the divisor of jumping lines Σ E of any E ∈ Q lf ( n ) , the moduli space of Gieseker‐semistable locally free sheaves of rank 2 on P 2 with( c 1 , c 2 ) = ( 0 , n ) , is reduced for n ≤ 4 . By a lemma of Artamkin this implies, that there are exactly n − 1A u t ( A 2 ) ‐orbits inM lf ( n ) ⊂ Q lf ( n ) , the subset of those E , which are trivial at a certain line l ∞ .