New Geometric Invariants Arising from Hodge Theory
The use of the Hodge line bundle, especially its positivity properties, in algebraic geometry is classical. The Hodge line bundle only sees the associated graded to the limiting mixed Hodge structures (LMHS's) that arise from the singular members in a family of algebraic varieties. This talk will introduce a new type of geometric object associated to the extension data in LMHS's (and not present for general MHS's) whose positivity properties play a central role in the application of Hodge theory to moduli. Their construction will be discussed and illustrated.
Talk given at the "Algebraic Geometry in Mexico" conference taking place at Puerta Escondido, December 2 - 7, 2018. Partly based on work in progress with Mark Green, Radu Laza and Colleen Robles.