{"docId":5602,"paperId":3990,"url":"https:\/\/epiga.episciences.org\/3990","doi":"10.46298\/epiga.2019.volume3.3990","journalName":"\u00c9pijournal de G\u00e9om\u00e9trie Alg\u00e9brique","issn":"","eissn":"2491-6765","volume":[{"vid":361,"name":"Volume 3"}],"section":[],"repositoryName":"arXiv","repositoryIdentifier":"1703.10441","repositoryVersion":3,"repositoryLink":"https:\/\/arxiv.org\/abs\/1703.10441v3","dateSubmitted":"2017-10-12 20:18:58","dateAccepted":"2019-06-26 11:22:35","datePublished":"2019-06-26 11:25:55","titles":["Q_l-cohomology projective planes and singular Enriques surfaces in\n characteristic two"],"authors":["Sch\u00fctt, Matthias"],"abstracts":["We classify singular Enriques surfaces in characteristic two supporting a rank nine configuration of smooth rational curves. They come in one-dimensional families defined over the prime field, paralleling the situation in other characteristics, but featuring novel aspects. Contracting the given rational curves, one can derive algebraic surfaces with isolated ADE-singularities and trivial canonical bundle whose Q_l-cohomology equals that of a projective plane. Similar existence results are developed for classical Enriques surfaces. We also work out an application to integral models of Enriques surfaces (and K3 surfaces).","Comment: 24 pages; v3: journal version, correcting 20 root types to 19 and ruling out the remaining type 4A_2+A_1 (in new section 11)"],"keywords":["Mathematics - Algebraic Geometry","Mathematics - Number Theory","14J28, 14J27"]}