Unirationality of moduli spaces of special cubic fourfolds and K3 surfaces

Howard Nuer

doi:10.14231/AG-2017-015

Unirationality of moduli spaces of special cubic fourfolds and K3 surfaces

Research output: Contribution to journal › Article › peer-review

Abstract

We provide explicit descriptions of the generic members of Hassett's divisors C_d in the moduli space C of smooth cubic fourfolds for relevant 18 ≤ d ≤ 38 and for d = 44. In doing so, we prove that C_d is unirational for these d. As a corollary, we prove that the moduli space Nd of polarized K3 surfaces of degree d is unirational for d = 14; 26; 38. The case d = 26 is entirely new, while the other two cases have been previously proven by Mukai.

Original language	English
Pages (from-to)	281-289
Number of pages	9
Journal	Algebraic Geometry
Volume	4
Issue number	3
DOIs	https://doi.org/10.14231/AG-2017-015
State	Published - 1 May 2017
Externally published	Yes

Keywords

Coble surfaces
Cubic fourfolds
Enriques surfaces
Hodge theory

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology

Access to Document

10.14231/AG-2017-015

Cite this

@article{4b6d85a4557d40ebab503674b8c5e84e,

title = "Unirationality of moduli spaces of special cubic fourfolds and K3 surfaces",

abstract = "We provide explicit descriptions of the generic members of Hassett's divisors Cd in the moduli space C of smooth cubic fourfolds for relevant 18 ≤ d ≤ 38 and for d = 44. In doing so, we prove that Cd is unirational for these d. As a corollary, we prove that the moduli space Nd of polarized K3 surfaces of degree d is unirational for d = 14; 26; 38. The case d = 26 is entirely new, while the other two cases have been previously proven by Mukai.",

keywords = "Coble surfaces, Cubic fourfolds, Enriques surfaces, Hodge theory",

author = "Howard Nuer",

note = "Publisher Copyright: {\textcopyright} Foundation Compositio Mathematica 2017.",

year = "2017",

month = may,

day = "1",

doi = "10.14231/AG-2017-015",

language = "אנגלית",

volume = "4",

pages = "281--289",

number = "3",

}

TY - JOUR

T1 - Unirationality of moduli spaces of special cubic fourfolds and K3 surfaces

AU - Nuer, Howard

N1 - Publisher Copyright: © Foundation Compositio Mathematica 2017.

PY - 2017/5/1

Y1 - 2017/5/1

N2 - We provide explicit descriptions of the generic members of Hassett's divisors Cd in the moduli space C of smooth cubic fourfolds for relevant 18 ≤ d ≤ 38 and for d = 44. In doing so, we prove that Cd is unirational for these d. As a corollary, we prove that the moduli space Nd of polarized K3 surfaces of degree d is unirational for d = 14; 26; 38. The case d = 26 is entirely new, while the other two cases have been previously proven by Mukai.

AB - We provide explicit descriptions of the generic members of Hassett's divisors Cd in the moduli space C of smooth cubic fourfolds for relevant 18 ≤ d ≤ 38 and for d = 44. In doing so, we prove that Cd is unirational for these d. As a corollary, we prove that the moduli space Nd of polarized K3 surfaces of degree d is unirational for d = 14; 26; 38. The case d = 26 is entirely new, while the other two cases have been previously proven by Mukai.

KW - Coble surfaces

KW - Cubic fourfolds

KW - Enriques surfaces

KW - Hodge theory

UR - http://www.scopus.com/inward/record.url?scp=85045426222&partnerID=8YFLogxK

U2 - 10.14231/AG-2017-015

DO - 10.14231/AG-2017-015

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85045426222

SN - 2313-1691

VL - 4

SP - 281

EP - 289

JO - Algebraic Geometry

JF - Algebraic Geometry

IS - 3

ER -

Unirationality of moduli spaces of special cubic fourfolds and K3 surfaces

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this