SOME GEOMETRIC PROPERTIES OF GOTZMANN COEFFICIENTS

• 영문명: SOME GEOMETRIC PROPERTIES OF GOTZMANN COEFFICIENTS
• 발행기관: 충청수학회
• 저자명: Jeaman Ahn
• 간행물 정보: 『Journal of the Chungcheong Mathematical Society』Volume 37, No. 2, 57~66쪽, 전체 10쪽
• 주제분류: 자연과학 > 자연과학일반
• 파일형태: PDF
• 발행일자: 2024.05.31

영문 초록

In this paper, we study how the Hilbert polynomial, associated with a reduced closed subscheme X of codimension 2 in PN, reveals geometric information about X. Although it is known that the Hilbert polynomial can tell us about the scheme’s degree and arithmetic genus, we find additional geometric information it can provide for smooth varieties of codimension 2. To do this, we introduce the concept of Gotzmann coefficients, which helps to extract more information from the Hilbert polynomial. These coefficients are based on the binomial expansion of values of the Hilbert function. Our method involves combining techniques from initial ideals and partial elimination ideals in a novel way. We show how these coefficients can determine the degree of certain geometric features, such as the singular locus appearing in a generic projection, for smooth varieties of codimension 2.

목차

1. Introduction

2. Gotzmann coefficients of Hilbert polynomials

3. Main results

References

키워드

Hilbert function generic projection Gotzmann regularity theorem Gotzmann coefficient partial elimination ideal