Families of Elliptic Curves in P3 and Bridgeland Stability

被引：7

作者：

Gallardo, Patricio ^{[1
]}

Lozano Huerta, Cesar ^{[2
]}

Schmidt, Benjamin ^{[3
]}

机构：

[1] Univ Georgia, Dept Math, Athens, GA 30602 USA

[2] CONACYT UNAM, Inst Matemat, Oaxaca De Juarez 6800, Oax, Mexico

[3] Univ Texas Austin, Dept Math, 2515 Speedway,RLM 8-100, Austin, TX 78712 USA

来源：

MICHIGAN MATHEMATICAL JOURNAL | 2018年 / 67卷 / 04期

关键词：

BOGOMOLOV-GIESEKER INEQUALITY; HILBERT SCHEME; EFFECTIVE CONE; MODULI; SPACE; THREEFOLDS; COMPLEXES; SHEAVES;

D O I：

10.1307/mmj/1538705132

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study wall crossings in Bridgeland stability for the Hilbert scheme of elliptic quartic curves in the three-dimensional projective space. We provide a geometric description of each of the moduli spaces we encounter, including when the second component of this Hilbert scheme appears. Along the way, we prove that the principal component of this Hilbert scheme is a double blowup with smooth centers of a Grassmannian, exhibiting a completely different proof of this known result by Avritzer and Vainsencher. This description allows us to compute the cone of effective divisors of this component.

引用

页码：787 / 813

页数：27

共 35 条

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[Anonymous], MACAULAY2 SOFTWARE S

[2]

[Anonymous], 1967, Amer. Math. Soc

[3] Bridgeland-stable moduli spaces for K-trivial surfaces [J].