Prym varieties and moduli of polarized Nikulin surfaces

被引：11

作者：

Farkas, Gavril ^{[1
]}

Verra, Alessandro ^{[2
]}

机构：

[1] Humboldt Univ, Inst Math, Unter Linden 6, D-10099 Berlin, Germany

[2] Univ Rome Tre, Dipartimento Matemat, I-00146 Rome, Italy

来源：

ADVANCES IN MATHEMATICS | 2016年 / 290卷

关键词：

Moduli space of curves; Prym variety; Nikulin K3 surface; K3; SURFACES; RATIONALITY; CURVES; CONE;

D O I：

10.1016/j.aim.2015.12.006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present a structure theorem for the moduli space R-7 of Prym curves of genus 7 as a projective bundle over the moduli space of 7-nodal rational curves. The existence of this parametrization implies the unirationality of R-7 and that of the moduli space of Nikulin surfaces of genus 7, as well as the rationality of the moduli space of Nikulin surfaces of genus 7 with a distinguished line. Using the results in genus 7, we then establish that R-8 is uniruled. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：314 / 328

页数：15

共 22 条

[1]

Bohning C., 2009, RATIONALITY PROBLEM

[2]

Boucksom S, 2013, J ALGEBRAIC GEOM, V22, P201

[3]

Bruns G., ARXIV151108468

[4]

Castelnuovo G., 1889, RENDICONTI R ACCAD L, V5, P130

[5]

CATANESE F, 1983, LECT NOTES MATH, V1008, P30

[6] ON THE TORELLI PROBLEM FOR PRYM VARIETIES [J].

DEBARRE, O .

AMERICAN JOURNAL OF MATHEMATICS, 1989, 111 (01) :111-134

[7]

Dolgachev I., 1996, J. Math. Sci, V81, P2599, DOI [10.1007/BF02362332, DOI 10.1007/BF02362332]

[8]

Dolgachev IV, 2008, PURE APPL MATH Q, V4, P501

[9] THE UNIRATIONALITY OF A5 [J].

DONAGI, R .

ANNALS OF MATHEMATICS, 1984, 119 (02) :269-307

[10] Moduli of theta-characteristics via Nikulin surfaces [J].

Farkas, Gavril ;

Verra, Alessandro .

MATHEMATISCHE ANNALEN, 2012, 354 (02) :465-496

← 1 2 3 →