Syzygies of Line Bundles on GIT Quotients

2015/09/01 by Krishna Hanumanthu, Anwesh Ray, Hanumanthu, Krishna +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #math.AG #msc:13A35 #msc:13A50 #msc:13D02 #msc:14C20 #msc:14L24 #msc:14L30

paper · pdf · doi:10.48550/arxiv.1509.00341

This paper is withdrawn due to an error in the proof of the crucial Lemma 2.1

arxiv created 2016/02/22 · arxiv updated 2016/02/23

Abstract

Let k be an algebraically closed field. Consider a reductive group G over k. Let X be a projective variety over k with a G-action and let L be a very ample G-linearized line bundle on X. Suppose that L descends to the GIT quotient of X by G. If L satisfies the property N_p one can ask if its descent also has N_p property. In this article, we show this is the case under certain conditions. We then apply our results to some cases of interest. As a consequence of our results, we show that if G is a finite group and L satisfies N_p property and its descent satisfies N₀ property then it satisfies N_p property as well under suitable conditions.

Related

• Syzygies of some GIT quotients
• Some conditions for descent of line bundles to GIT quotients (G/B\n \× G/B \× G/B)//G
• The GIT-equivalence for G-line bundles
• Descent of line bundles to GIT quotients of flag varieties by maximal torus
• Variation of Stratifications From Toric GIT