Timeline for Geometric meaning of Koszul modules

9 events

when toggle format	what		by	license	comment
Dec 14, 2019 at 0:35	comment	added	mkemeny		These two conditions are basically the same in our setting, see the top of page 8 of arxiv.org/pdf/1408.4164.pdf
Dec 12, 2019 at 23:57	comment	added	Li Li		@mkemeny But those propositions induce that $L$ does not satisfy $N_p$(in fact $N_{p-1}$ in my situation). This doesn't imply the nonvanishment of $K_{p,2}$, right?
Nov 24, 2019 at 4:00	comment	added	mkemeny		Hi ! This is a result from Koh-Stillman's paper "Linear Syzygies and Line Bundles on an Algebraic Curve", see Prop. 3.6. You can also look at Chapter 4.4 of Aprodu-Nagel's book "Koszul Cohomology and Algebraic Geometry", in particular Theorem 4.36.
Nov 17, 2019 at 17:47	comment	added	meh		You will have to do some digging yourself, but there is a paper of Green and Lazarsfeld in which they show how to construct non-zero Koszul cohomology classes from points in special position w.r.t a line bundle. 'not p+1 very ample' means that there are p+1 points in special position relative to L. The construction of the class is explicit and imho, geometric. Happy hunting.
S Nov 17, 2019 at 16:58	history	suggested	ABIM		More tags for more outreach.
Nov 17, 2019 at 16:57	review	Suggested edits
S Nov 17, 2019 at 16:58
Nov 17, 2019 at 16:49	history	edited	Amir Sagiv	CC BY-SA 4.0	Link and formatting
Nov 17, 2019 at 16:45	review	First posts
Nov 17, 2019 at 16:49
Nov 17, 2019 at 16:43	history	asked	Li Li	CC BY-SA 4.0