Geodesic
Threefolds fibred by mirror sextic double planes
Canadian journal of mathematics, Tome 73 (2021) no. 5, pp. 1305-1346

Voir la notice de l'article provenant de la source Cambridge

DOI

We present a systematic study of threefolds fibred by K3 surfaces that are mirror to sextic double planes. There are many parallels between this theory and the theory of elliptic surfaces. We show that the geometry of such threefolds is controlled by a pair of invariants, called the generalized functional and generalized homological invariants, and we derive an explicit birational model for them, which we call the Weierstrass form. We then describe how to resolve the singularities of the Weierstrass form to obtain the “minimal form”, which has mild singularities and is unique up to birational maps in codimension 2. Finally, we describe some of the geometric properties of threefolds in minimal form, including their singular fibres, canonical divisor, and Betti numbers.
DOI : 10.4153/S0008414X20000498
Mots-clés : K3 surface, threefold, fibration 
Kooistra, Remkes; Thompson, Alan. Threefolds fibred by mirror sextic double planes. Canadian journal of mathematics, Tome 73 (2021) no. 5, pp. 1305-1346. doi: 10.4153/S0008414X20000498
@article{10_4153_S0008414X20000498,
     author = {Kooistra, Remkes and Thompson, Alan},
     title = {Threefolds fibred by mirror sextic double planes},
     journal = {Canadian journal of mathematics},
     pages = {1305--1346},
     year = {2021},
     volume = {73},
     number = {5},
     doi = {10.4153/S0008414X20000498},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X20000498/}
}
TY  - JOUR
AU  - Kooistra, Remkes
AU  - Thompson, Alan
TI  - Threefolds fibred by mirror sextic double planes
JO  - Canadian journal of mathematics
PY  - 2021
SP  - 1305
EP  - 1346
VL  - 73
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/S0008414X20000498/
DO  - 10.4153/S0008414X20000498
ID  - 10_4153_S0008414X20000498
ER  - 
%0 Journal Article
%A Kooistra, Remkes
%A Thompson, Alan
%T Threefolds fibred by mirror sextic double planes
%J Canadian journal of mathematics
%D 2021
%P 1305-1346
%V 73
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/S0008414X20000498/
%R 10.4153/S0008414X20000498
%F 10_4153_S0008414X20000498

Cité par Sources :