### April

M T W T F S S

1

2

3

4

5

6

7

8

9

10

11

13

14

15

16

17

18

19

20

21

22

23

24

25

26

29

30

Responsabili:

Nel calendario si indicano i seminari di geometria algebrica e altre attività di interesse, organizzate dall'Università e dal Politecnico di Torino.

## Evento

Titolo: The range of all regularities for a given Hilbert function
Quando: 20/02/2019 - 15:00
Dove: Palazzo Campana - TORINO
Aula: Aula 4
Relatore: Francesca Cioffi
Afferenza: Università di Napoli
Locandina:

## Descrizione:

Abstract: Given the Hilbert function $u$ of a closed subscheme of a projective
space over an infinite field $K$, let $m_u$ and $M_u$ be,
respectively, the minimum and the maximum among all the
Castelnuovo-Mumford regularities of schemes with Hilbert function~$u$.
I show that, for every integer $m$ such that $m_u \leq m \leq M_u$,
there exists a scheme with Hilbert function $u$ and
Castelnuovo-Mumford regularity $m$. As a consequence, the analogous
algebraic result for an O-sequence $f$ and homogeneous polynomial
ideals over $K$ with Hilbert function $f$ holds too.

Although this result does not need any explicit computation, I also
describe how to compute a scheme with the above requested properties.
Precisely, I give a method to construct a strongly stable ideal
defining such a scheme.

## Sede

Sede:
Indirizzo: Via Carlo Alberto 10
CAP: 10123
Città: TORINO