Department of Mathematics,
University of California San Diego
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Math 211A - Algebra Seminar
Fuxiang Yang
University of Notre Dame du Lac
Recent progress on the Eisenbud-Huneke-Ulrich conjecture
Abstract:
Over a polynomial ring, an ideal I is said to be linearly presented if its first syzygy module is generated by linear relations. More generally, the resolution of I is linear for p steps if this linearity continues through the first p steps. In this talk, we explore some fundamental properties of ideals with partially linear minimal free resolution, such as asymptotic behavior of powers, Castelnuovo-Mumford regularity, and lower bounds on the number of minimal generators. In particular, we prove the Eisenbud-Ulrich conjecture on powers of linearly presented ideals and establish a linear effective bound toward the more general Eisenbud-Huneke-Ulrich conjecture.
Host: Karthik Ganapathy
October 19, 2026
3:00 PM
APM 7321
Research Areas
Algebra****************************
