PIMS Emergent Research Seminar: Emanuela Marangone

Topic

Lefschetz Properties for Artinian Complete Intersections

Speakers

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Emanuela Marangone
PIMS Postdoctoral Fellow, University of Manitoba

Details

In this talk, we will introduce the Weak and the Strong Lefschetz Properties (WLP and SLP) focusing on Artinian complete intersections. A famous result of Stanley shows that every Artinian monomial complete intersection over a field of characteristic zero has the SLP and the WLP.

However, this result does not hold in positive characteristics. In the first part of the talk, we will present results on monomial complete intersections with WLP in characteristic p, and give a complete classification for p=2.

In the second part of the talk, we will work over characteristic zero.  It remains an open conjecture whetherevery complete intersection has WLP. Harima, Migliore, Nagel, and Watanabe prove the conjecture for complete intersections of height 3, and Boij, Migliore, Miró-Roig, and Nagel introduce the study of the non-Lefschetz locus. We will address a similar question for forms of degree 2 instead of lines. Specifically, we will show that every complete intersection of height 3 has the Strong Lefschetz Property in degree 2 and study the non-Lefschetz locus of conics.

Additional Information

This seminar takes places across multiple time zones: 9:30 AM PT/ 10:30 AM MT / 11:30 AM CT

Register via Zoom to receive the link (and reminders) for this event and the rest of the series.

Jump to Event Details
Event Type
Scientific, Seminar
Date
January 29, 2025
Time
-
Location
Online
Zoom
Registration

This seminar takes places across multiple time zones: 9:30 AM PT/ 10:30 AM MT / 11:30 AM CT. Register via Zoom to receive the link (and reminders) for this event and the rest of the series.

register