Imagine a complex, smooth surface that is triple embedded. I'm interested in the limit at which the surface degenerates into a reducible (but reduced) surface. In other words, I have a family of surfaces.

begin {eqnarray}

pi: mathcal {S} rightarrow Delta,

end {eqnarray}

Where $ Delta $ is parameterized by a complex variable $ t $, and $ S_t = pi ^ {- 1} (t) $ is smooth for $ 0 0 $ and, $ S_0 $ is the degenerate surface.

My questions are:

1- What kind of rank one coherent sheaf on $ S_0 $ may be the limit of a bundle of cables $ S_t $, Is it true that any element of $ Pic (S_0) $ are limit of the line bundles $ S_t $?

2- Assume that I select trunk bundles over each component of $ S_0 $ they are not a limit of a line bundle, so it is equivalent $ (1.1) $ drive in $ S_0 $, Then I deform myself $ S_0 $ to something smooth $ S_t $What happens to these (1,1) cycles?

For some physical reasons, I expect the answer to the first question to be yes, and for the second I hope it should become one $ (2.0) $ Cycle after deformation.

Please let me know if there are references to the above questions that are not too abstract (for a physics student to read).

Thanks.