  We use topological methods to study various semicontinuity properties of
spectra of singular points of plane algebraic curves and of polynomials in two
variables at infinity. Using Seifert forms and the Tristram--Levine signatures
of links, we reprove (in a slightly weaker version) a result obtained by
Steenbrink and Varchenko on semicontinuity of spectrum at infinity. We also
relate the spectrum at infinity of a polynomial with spectra of singular points
of a chosen fiber.
