The minimal model program for the Hilbert scheme of points on P2 and Bridgeland stability

Daniele Arcara, Aaron Bertram, Izzet Coskun, Jack William Huizenga

Research output: Contribution to journalArticle

50 Citations (Scopus)

Abstract

In this paper, we study the birational geometry of the Hilbert scheme P2[n] of n-points on P2. We discuss the stable base locus decomposition of the effective cone and the corresponding birational models. We give modular interpretations to the models in terms of moduli spaces of Bridgeland semi-stable objects. We construct these moduli spaces as moduli spaces of quiver representations using G.I.T. and thus show that they are projective. There is a precise correspondence between wall-crossings in the Bridgeland stability manifold and wall-crossings between Mori cones. For n ≤ 9, we explicitly determine the walls in both interpretations and describe the corresponding flips and divisorial contractions.

Original languageEnglish (US)
Pages (from-to)580-626
Number of pages47
JournalAdvances in Mathematics
Volume235
DOIs
StatePublished - Mar 1 2013

Fingerprint

Hilbert Scheme
Minimal Model
Moduli Space
Cone
Quiver Representation
Flip
Locus
Contraction
Correspondence
Decompose
Model
Interpretation

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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The minimal model program for the Hilbert scheme of points on P2 and Bridgeland stability. / Arcara, Daniele; Bertram, Aaron; Coskun, Izzet; Huizenga, Jack William.

In: Advances in Mathematics, Vol. 235, 01.03.2013, p. 580-626.

Research output: Contribution to journalArticle

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