The maximum cut problem on blow-ups of multiprojective spaces release_vdh5huexzfhz3dspcsyqfpu7me

by Mauricio Junca Mauricio Velasco

Released as a article .

2012  

Abstract

The maximum cut problem for a quintic del Pezzo surface Bl_4(P^2) asks: Among all partitions of the 10 exceptional curves into two disjoint sets, what is the largest possible number of pairwise intersections? In this article we show that the answer is twelve. More generally, we obtain bounds for the maximum cut problem for the minuscule varieties X_a,b,c:= Bl_b+c(P^c-1)^a-1 studied by Mukai and Castravet-Tevelev and show that these bounds are asymptotically sharp for infinite families. We prove our results by constructing embeddings of the classes of (-1)-divisors on these varieties which are optimal for the semidefinite relaxation of the maximum cut problem on graphs proposed by Goemans and Williamson. These results give a new optimality property of the Weyl orbits of root systems of type A,D and E.
In text/plain format

Archived Files and Locations

application/pdf  553.2 kB
file_bunynfvbufhh5oep22pddknhoy
archive.org (archive)
Read Archived PDF
Preserved and Accessible
Type  article
Stage   submitted
Date   2012-07-17
Version   v1
Language   en ?
arXiv  1207.4027v1
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: de5a60e8-7a6f-4f0a-9062-e3e5d0b48de7
API URL: JSON