Description

Date and Time: Tuesday 1st September 2020, 5:30 pm IST - 6:30 pm IST

(joining time : 5:15 pm IST - 5:30 pm IST)

Google Meet link: https://meet.google.com/yqu-mvvy-jrs

Speaker: Matteo Varbaro, University of Genoa

Title: F-splittings of the polynomial ring and compatibly split

homogeneous ideals

Abstract: A polynomial ring R in n variables over a field K of positive

characteristic is F-split. It has many F-splittings. When K is a perfect

field every F-splitting is given by a polynomial g in R with the monomial

u^{p-1} in its support (where u is the product of all the variables)

occurring with coefficient 1, plus a further condition, which is not

needed if g is homogeneous (w.r.t. any positive grading). Fixed an

F-splitting s : R -> R, an ideal I of R such that s(I) is contained in I

is said compatibly split (w.r.t. the F-splittings). In this case R/I is

F-split. Furthermore, by Fedderâ€™s criterion when I is a homogeneous ideal

of R, R/I is F-split if and only if I is compatibly split for some

F-splitting s : R -> R. If, moreover, u^{p-1} is the initial monomial of

the associated polynomial g of s w.r.t. some monomial order, then in(I) is

a square-free monomial idealâ€¦ In this talk I will survey these facts (some

of them classical, some not so classical), and make some examples,

focusing especially on determinantal ideals.

(joining time : 5:15 pm IST - 5:30 pm IST)

Google Meet link: https://meet.google.com/yqu-mvvy-jrs

Speaker: Matteo Varbaro, University of Genoa

Title: F-splittings of the polynomial ring and compatibly split

homogeneous ideals

Abstract: A polynomial ring R in n variables over a field K of positive

characteristic is F-split. It has many F-splittings. When K is a perfect

field every F-splitting is given by a polynomial g in R with the monomial

u^{p-1} in its support (where u is the product of all the variables)

occurring with coefficient 1, plus a further condition, which is not

needed if g is homogeneous (w.r.t. any positive grading). Fixed an

F-splitting s : R -> R, an ideal I of R such that s(I) is contained in I

is said compatibly split (w.r.t. the F-splittings). In this case R/I is

F-split. Furthermore, by Fedderâ€™s criterion when I is a homogeneous ideal

of R, R/I is F-split if and only if I is compatibly split for some

F-splitting s : R -> R. If, moreover, u^{p-1} is the initial monomial of

the associated polynomial g of s w.r.t. some monomial order, then in(I) is

a square-free monomial idealâ€¦ In this talk I will survey these facts (some

of them classical, some not so classical), and make some examples,

focusing especially on determinantal ideals.

Date

Tue, September 1, 2020

Start Time

5:30pm-6:30pm IST

Duration

1 hour

Priority

5-Medium

Access

Public

Created by

DEFAULT ADMINISTRATOR

Updated

Mon, August 31, 2020 11:36am IST