BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Matteo Varbaro (University of Genoa) DTSTART:20200901T120000Z DTEND:20200901T130000Z DTSTAMP:20260423T020954Z UID:VCAS/17 DESCRIPTION:Title: F- splittings of the polynomial ring and compatibly split homogeneous ideals< /a>\nby Matteo Varbaro (University of Genoa) as part of IIT Bombay Virtual Commutative Algebra Seminar\n\n\nAbstract\nA polynomial ring R in n varia bles over a field K of positive characteristic is F-split. It has many F-s plittings. When K is a perfect field every F-splitting is given by a polyn omial g in R with the monomial u^{p-1} in its support (where u is the prod uct of all the variables) occurring with coefficient 1\, plus a further co ndition\, which is not needed if g is homogeneous (w.r.t. any positive gra ding). 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-splitting s). In th is case R/I is F-split. Furthermore\, by Fedder’s criterion when I is a homogeneous ideal of R\, R/I is F-split if and only if I is compatibly spl it 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 ideal… In this talk I will survey these facts (some of them classical\, some not so classical)\, and make so me examples\, focusing especially on determinantal ideals.\n LOCATION:https://researchseminars.org/talk/VCAS/17/ END:VEVENT END:VCALENDAR