Báo cáo viên: Dr. Le Ngoc Long (University of Education - Hue University)
Thời gian: 16h30, ngày 27/3/2025
Địa điểm: Báo cáo thực hiện trực tiếp tại: Phòng 612 nhà A6 - Viện Toán học
và Online (Join Zoom Meeting) tại link: https://zoom.us/j/99636681387?pwd=0WscBnehOJig68SqctGluVuA3RwraE.1
Tóm tắt: Given a zero-dimensional scheme X in the n-dimensional projective space over a field K, we are interesting in studying the geometry of X, focusing on the utilization of differential invariants. Specifically, we explore the connection between these invariants and the geometric properties of X, including curvilinearity, uniformity, and the complete intersection property.
A central differential invariant is the module of Kähler differential m-forms $Omega^m_R$, associated with the homogeneous coordinate ring R of X. The relationship between $Omega^m_R$ and the smoothness of X has been known for a long time, and it can be effectively characterized via the Hilbert polynomials $Omega^m_R$. Based on recent studies of the Hilbert functions of these modules, we aim to extract deeper insights into the geometric attributes of X.
This presentation will begin with a summary of computations concerning the Hilbert functions of $Omega^m_R$ for zero dimensional schemes. Subsequently, we will discuss the connections between these modules and the curvilinear and uniform properties of X. Finally, we examine the relationship between the first nonzero Fitting ideal of $Omega^1_R$ and the complete intersection property of X. |
