MINIMAL CASTELNUOVO-MUMFORD REGULARITY FOR A GIVEN HILBERT POLYNOMIAL
| Autor: | Francesca Cioffi, M. Grazia Marinari, Paolo Lella, Margherita Roggero |
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| Přispěvatelé: | Cioffi, Francesca, P., Lella, M. G., Marinari, M., Roggero |
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Pure mathematics
Polynomial Constructive proof General Mathematics Hilbert polynomial symbols.namesake Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry Castelnuovo–Mumford regularity 14Q99 68W30 11Y55 FOS: Mathematics regularity of a Hilbert function Ideal (ring theory) Algebraically closed field Castelnuovo-Mumford regularity Hilbert ynomial Algebraic Geometry (math.AG) minimal function Mathematics Borel ideal Hilbert series and Hilbert polynomial Mathematics::Commutative Algebra Null (mathematics) symbols closed projective subscheme Borel set |
| Popis: | Let $K$ be an algebraically closed field of null characteristic and $p(z)$ a Hilbert polynomial. We look for the minimal Castelnuovo-Mumford regularity $m_{p(z)}$ of closed subschemes of projective spaces over $K$ with Hilbert polynomial $p(z)$. Experimental evidences led us to consider the idea that $m_{p(z)}$ could be achieved by schemes having a suitable minimal Hilbert function. We give a constructive proof of this fact. Moreover, we are able to compute the minimal Castelnuovo-Mumford regularity $m_p(z)^{\varrho}$ of schemes with Hilbert polynomial $p(z)$ and given regularity $\varrho$ of the Hilbert function, and also the minimal Castelnuovo-Mumford regularity $m_u$ of schemes with Hilbert function $u$. These results find applications in the study of Hilbert schemes. They are obtained by means of minimal Hilbert functions and of two new constructive methods which are based on the notion of growth-height-lexicographic Borel set and called ideal graft and extended lifting. Comment: 21 pages. Comments are welcome. More concise version with a slight change in the title. A further revised version has been accepted for publication in Experimental Mathematics |
| Databáze: | OpenAIRE |
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