Leírás
Abstract: Let U ⊆ C^n be an open subset. The Bergman space A^2(U) is the
Hilbert space of holomorphic functions on U which are square-integrable
with respect to the Euclidean volume form dV. A theorem of Wiegerinck
asserts that in dimension one the Bergman space of an open subset U ⊂ C
is either infinite dimensional or trivial. Recently, this has been
generalized to holomorphic vector bundles over the projective line by R.
Szőke and later to vector bundles over any compact Riemann surface by A.
Gallagher, P. Gupta, L. Vivas.
The topic of this talk will be to prove our even more recent result
extending this dichotomy to the case of affine and projective algebraic
curves. To do so I will recall the fundamentals of the theory of
algebraic curves and introduce Bergman spaces. Then I discuss the
extension of the results above to the case of certain singular volume
forms on a Riemann surface associated to divisors and show how this
yields versions of Wiegerinck’s theorem for algebraic curves.
Joint work with Alexander A. Kubasch and Róbert Szőke.
For Zoom access, please contact Viktória Földvári.