Geodesic
On the stability of the universal quotient bundle restricted to congruences of low degree of 𝔾(1,3)
Arrondo, Enrique1  ; Cobo, Sofía1
1 Departamento de Álgebra, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 9 (2010) no. 3, pp. 503-522

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We study the semistability of Q| S , the universal quotient bundle on 𝔾(1,3) restricted to any smooth surface S (called congruence). Specifically, we deduce geometric conditions for a congruence S, depending on the slope of a saturated linear subsheaf of Q| S . Moreover, we check that the Dolgachev-Reider Conjecture (i.e. the semistability of Q| S for nondegenerate congruences S) is true for all the congruences of degree less than or equal to 10. Also, when the degree of a congruence S is less than or equal to 9, we compute the highest slope reached by the linear subsheaves of Q| S .

Classification : 14J60, 14M07, 14M15

Arrondo, Enrique 1 ; Cobo, Sofía 1

1 Departamento de Álgebra, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain 
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     title = {On the stability of the universal quotient bundle restricted to congruences of low degree of $\mathbb{G}{\bf (1,3)}$},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {503--522},
     publisher = {Scuola Normale Superiore, Pisa},
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Arrondo, Enrique; Cobo, Sofía. On the stability of the universal quotient bundle restricted to congruences of low degree of $\mathbb{G}{\bf (1,3)}$. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 9 (2010) no. 3, pp. 503-522. http://geodesic.mathdoc.fr/item/ASNSP_2010_5_9_3_503_0/