4 papers
Log Conifold Transitions
Rodolfo Aguilar
We define log conifold transitions for Fano threefold pairs of index two and study their deformation theory. Relying on the recent solution to the relative Clemens conjectures in t…
The relative Clemens Conjectures for -log Calabi-Yau threefolds
Rodolfo Aguilar
We formulate a relative analogue of the Clemens conjectures for 1/2-log Calabi-Yau threefold pairs (X,Y) (where K_X+2Y is isomorphic to O_X). This framework rests on the restoratio…
Infinitesimal invariants of mixed Hodge structures II: Log Clemens conjecture and log connectivity
Rodolfo Aguilar
Following previous work, we continue the study of infinitesimal methods in mixed Hodge theory. In the first part, inspired by the deformation theory of curves on Calabi-Yau threefo…
Lagrangian interpretation of Abel-Jacobi mappings associated to Fano threefolds
Rodolfo Aguilar, Mark Green, Phillip Griffiths
Using the general framework due to Donagi-Markman \cite{DM} and Markushevich \cite{M} we shall derive an expression for the differential of Abel-Jacobi mappings on Fano threefolds.…