☆ 4.2 Article

NEW MODULI SPACES OF ONE-DIMENSIONAL SHEAVES ON P3

NAGOYA MATHEMATICAL JOURNAL (2023)

Journal

NAGOYA MATHEMATICAL JOURNAL

Volume -, Issue -, Pages -

Publisher

CAMBRIDGE UNIV PRESS

DOI: 10.1017/nmj.2023.26

Keywords

14D20

Categories

Mathematics

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Abstract

This paper focuses on the study of a one-dimensional family of Bridgeland stability conditions on P-n, named Euler stability condition. It is conjectured that the Euler stability condition converges to Gieseker stability for coherent sheaves. The author first identifies Euler stability conditions with double-tilt stability conditions on P-3 and then investigates the moduli of one-dimensional sheaves. The results include asymptotic results, boundedness for walls, and explicit computation of walls and wall-crossings for sheaves supported on rational curves of degrees 3 and 4.

We define a one-dimensional family of Bridgeland stability conditions on P-n, named Euler stability condition. We conjecture that the Euler stability condition converges to Gieseker stability for coherent sheaves. Here, we focus on P-3, first identifying Euler stability conditions with double-tilt stability conditions, and then we consider moduli of one-dimensional sheaves, proving some asymptotic results, boundedness for walls, and then explicitly computing walls and wall-crossings for sheaves supported on rational curves of degrees 3 and 4.

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