Details
| Original language | English |
|---|---|
| Pages (from-to) | 159-213 |
| Number of pages | 55 |
| Journal | Algebraic Geometry |
| Volume | 9 |
| Issue number | 2 |
| Publication status | Published - Mar 2022 |
Abstract
In this paper, we investigate two stratifications of the moduli space of elliptically fibred K3 surfaces. The first comes from Shimada's classification of connected components of the moduli of elliptically fibred K3 surfaces and is closely related to the root lattices of the fibration. The second is the monodromy stratification defined by Bogomolov, Petrov and Tschinkel. The main result of the paper is a classification of all positivedimensional ambi-typical strata, that is, strata which are both Shimada root strata and monodromy strata. We also discuss the relationship with moduli spaces of latticepolarised K3 surfaces. The appendix by M. Kirschmer contains computational results about the 1-dimensional ambi-typical strata.
Keywords
- Elliptic surfaces, K3 surfaces, Moduli spaces, Monodromy
ASJC Scopus subject areas
- Mathematics(all)
- Geometry and Topology
- Mathematics(all)
- Algebra and Number Theory
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Algebraic Geometry, Vol. 9, No. 2, 03.2022, p. 159-213.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Moduli of elliptic K3 surfaces
T2 - Monodromy and Shimada root lattice strata
AU - Hulek, Klaus
AU - Lönne, Michael
A2 - Kirschmer, Markus
N1 - Funding Information: The first author is grateful to DFG for partial support under grant Hu 337/7-1. The second author acknowledges the support of the ERC 2013 Advanced Research Grant 340258-TADMICAMT.
PY - 2022/3
Y1 - 2022/3
N2 - In this paper, we investigate two stratifications of the moduli space of elliptically fibred K3 surfaces. The first comes from Shimada's classification of connected components of the moduli of elliptically fibred K3 surfaces and is closely related to the root lattices of the fibration. The second is the monodromy stratification defined by Bogomolov, Petrov and Tschinkel. The main result of the paper is a classification of all positivedimensional ambi-typical strata, that is, strata which are both Shimada root strata and monodromy strata. We also discuss the relationship with moduli spaces of latticepolarised K3 surfaces. The appendix by M. Kirschmer contains computational results about the 1-dimensional ambi-typical strata.
AB - In this paper, we investigate two stratifications of the moduli space of elliptically fibred K3 surfaces. The first comes from Shimada's classification of connected components of the moduli of elliptically fibred K3 surfaces and is closely related to the root lattices of the fibration. The second is the monodromy stratification defined by Bogomolov, Petrov and Tschinkel. The main result of the paper is a classification of all positivedimensional ambi-typical strata, that is, strata which are both Shimada root strata and monodromy strata. We also discuss the relationship with moduli spaces of latticepolarised K3 surfaces. The appendix by M. Kirschmer contains computational results about the 1-dimensional ambi-typical strata.
KW - Elliptic surfaces
KW - K3 surfaces
KW - Moduli spaces
KW - Monodromy
UR - http://www.scopus.com/inward/record.url?scp=85125711744&partnerID=8YFLogxK
U2 - 10.14231/AG-2022-006
DO - 10.14231/AG-2022-006
M3 - Article
VL - 9
SP - 159
EP - 213
JO - Algebraic Geometry
JF - Algebraic Geometry
SN - 2313-1691
IS - 2
ER -