We study the semistability of , the universal quotient bundle on (1,3) restricted to any smooth surface (called congruence). Specifically, we deduce geometric conditions for a congruence , depending on the slope of a saturated linear subsheaf of . Moreover, we check that the Dolgachev-Reider Conjecture (i.e. the semistability of for nondegenerate congruences ) is true for all the congruences of degree less than or equal to 10. Also, when the degree of a congruence is less than or equal to 9, we compute the highest slope reached by the linear subsheaves of .
@article{ASNSP_2010_5_9_3_503_0, author = {Arrondo, Enrique and Cobo, Sof\'\i a}, 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}, volume = {Ser. 5, 9}, number = {3}, year = {2010}, zbl = {1202.14038}, mrnumber = {2722653}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2010_5_9_3_503_0/} }
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://www.numdam.org/item/ASNSP_2010_5_9_3_503_0/
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