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Duality, Bridgeland wall-crossing and flips of secant varieties

Cristian Martinez

Department of Mathematics, University of California, Santa Barbara, South Hall, Room 6607, Santa Barbara, CA 93106-3080, USA

E-mail Address: martinez@math.ucsb.edu

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https://doi.org/10.1142/S0129167X17500112Cited by:7 (Source: Crossref)

Abstract

Let $v_{d} (ℙ^{2}) \subset | 𝒪_{ℙ^{2}} (d) |$ denote the $d$ -uple Veronese surface. After studying some general aspects of the wall-crossing phenomena for stability conditions on surfaces, we are able to describe a sequence of flips of the secant varieties of $v_{d} (ℙ^{2})$ by embedding the blow-up ${bl}_{v_{d} (ℙ^{2})} | 𝒪_{ℙ^{2}} (d) |$ into a suitable moduli space of Bridgeland semistable objects on $ℙ^{2}$ .

Keywords:

AMSC: 14D20, 14E30, 18E30

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