Abstract

The Clemens-Schmid sequence is a four-term exact sequence that relates the cohomology of a general fibre to the cohomology of the special fibre in a degeneration, and encodes useful information about the structure of the central fibre and the action of monodromy. I will present a candidate mirror to this sequence, which contains various information about the cohomology of a fibration. Based upon this, I will formulate a mirror conjecture relating the terms of the Clemens-Schmid sequence for a degeneration of a Calabi-Yau to the terms of the mirror sequence describing the structure of a fibration on the mirror Calabi-Yau. Finally, I will present illustrative examples from mirror symmetry for K3 surfaces and Calabi-Yau threefolds as evidence for this conjecture. This is joint work with Charles Doran.