Arrondo Esteban, EnriqueCobo Pablos, Sofía2023-06-202023-06-2020100391-173Xhttps://hdl.handle.net/20.500.14352/42088We study the semistability of Q vertical bar 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 vertical bar s. Moreover, we check that the Dolgachev-Reider Conjecture (i.e. the semistability of Q vertical bar 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 vertical bar s.engjournal articlehttp://annaliscienze.sns.it/public/pdf/abstracts/2010/Abstract_03_F3.pdfrestricted access512.7Smooth surfacesLinesGeometria algebraica1201.01 Geometría Algebraica