{"abstracts":[{"sha1":"651365c0c6441efb0e97ffb955a628587a3280e4","content":"A threefold isogenous to a product of curves X is a quotient of a product\nof three compact Riemann surfaces of genus at least two by the free action of a\nfinite group. In this paper we study these threefolds under the assumption that\nthe group acts diagonally on the product. We show that the classification of\nthese threefolds is a finite problem, present an algorithm to classify them for\na fixed value of χ( O_X) and explain a method to determine their\nHodge numbers. Running an implementation of the algorithm we achieve the full\nclassification of threefolds isogenous to a product of curves with\nχ( O_X)=-1, under the assumption that the group acts faithfully on\neach factor.","mimetype":"text/plain","lang":"en"},{"sha1":"e0806b3b4f6bd7bb176d163cc9d75aa0012a9966","content":"A threefold isogenous to a product of curves $X$ is a quotient of a product\nof three compact Riemann surfaces of genus at least two by the free action of a\nfinite group. In this paper we study these threefolds under the assumption that\nthe group acts diagonally on the product. We show that the classification of\nthese threefolds is a finite problem, present an algorithm to classify them for\na fixed value of $\\chi(\\mathcal O_X)$ and explain a method to determine their\nHodge numbers. Running an implementation of the algorithm we achieve the full\nclassification of threefolds isogenous to a product of curves with\n$\\chi(\\mathcal O_X)=-1$, under the assumption that the group acts faithfully on\neach factor.","mimetype":"application/x-latex","lang":"en"}],"refs":[],"contribs":[{"index":0,"raw_name":"Davide Frapporti","role":"author"},{"index":1,"raw_name":"Christian Gleissner","role":"author"}],"license_slug":"ARXIV-1.0","language":"en","version":"v2","ext_ids":{"arxiv":"1412.6365v2"},"release_year":2015,"release_date":"2015-01-14","release_stage":"submitted","release_type":"article","webcaptures":[],"filesets":[],"files":[{"release_ids":["fet2ckgdjvez3gpudwbgxdsdxq"],"mimetype":"application/pdf","urls":[{"url":"https://arxiv.org/pdf/1412.6365v2.pdf","rel":"repository"},{"url":"https://web.archive.org/web/20200912132028/https://arxiv.org/pdf/1412.6365v2.pdf","rel":"webarchive"}],"sha256":"61273586b80157f1e2d75c06cfe749dd87a24feef47522c821576eb1cd26b206","sha1":"71f0c2d9e9960a6065d10f91b02d7da7f400df4b","md5":"d65f4cfa7075842c526e8754e6a9d209","size":280075,"revision":"95de3606-7f62-4822-866b-c4c53f6aaa5a","ident":"j6n2xaapyndjzmvu2fqor4n2oa","state":"active"}],"work_id":"awxfqkg2ejhh7bcazfjusvu43y","title":"On Threefolds Isogenous to a Product of Curves","state":"active","ident":"fet2ckgdjvez3gpudwbgxdsdxq","revision":"19315d89-bf09-4ea1-bd86-4e3fb170f2eb","extra":{"arxiv":{"base_id":"1412.6365","categories":["math.AG"],"comments":"18 pages, 1 table; v2: improved exposition, results unchanged; v3:\n final version, improved exposition, results unchanged"},"superceded":true}}