{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T14:07:07Z","timestamp":1762870027845,"version":"build-2065373602"},"reference-count":0,"publisher":"European Mathematical Society - EMS - Publishing House GmbH","issue":"10","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Eur. Math. Soc."],"published-print":{"date-parts":[[2014,10,29]]},"abstract":"<jats:p>\n                    We take up the study of the Brill-Noether loci\n                    <jats:inline-formula>\n                      <jats:tex-math>W^r(L,X):=\\{\\eta\\in \\mathrm {Pic}^0(X)\\ |\\ h^0(L\\otimes\\eta)\\ge r+1\\}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , where\n                    <jats:inline-formula>\n                      <jats:tex-math>X<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    is a smooth projective variety of dimension\n                    <jats:inline-formula>\n                      <jats:tex-math>&gt;1<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    ,\n                    <jats:inline-formula>\n                      <jats:tex-math>L\\in \\mathrm {Pic}(X)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , and\n                    <jats:inline-formula>\n                      <jats:tex-math>r\\ge 0<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    is an integer.\n                  <\/jats:p>\n                  <jats:p>\n                    By studying the infinitesimal structure of these loci and the Petri map (defined in analogy with the case of curves), we obtain lower bounds for\n                    <jats:inline-formula>\n                      <jats:tex-math>h^0(K_D)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , where\n                    <jats:inline-formula>\n                      <jats:tex-math>D<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    is a divisor that moves linearly on a smooth projective variety\n                    <jats:inline-formula>\n                      <jats:tex-math>X<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    of maximal Albanese dimension. In this way we sharpen the results of [Xi] and we generalize them to dimension\n                    <jats:inline-formula>\n                      <jats:tex-math>&gt;2<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    .\n                  <\/jats:p>\n                  <jats:p>\n                    In the\n                    <jats:inline-formula>\n                      <jats:tex-math>2<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    -dimensional case we prove an existence theorem: we define a Brill-Noether number\n                    <jats:inline-formula>\n                      <jats:tex-math>\\rho(C, r)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    for a curve\n                    <jats:inline-formula>\n                      <jats:tex-math>C<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    on a smooth surface\n                    <jats:inline-formula>\n                      <jats:tex-math>X<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    of maximal Albanese dimension and we prove, under some mild additional assumptions, that if\n                    <jats:inline-formula>\n                      <jats:tex-math>\\rho(C, r)\\ge 0<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    then\n                    <jats:inline-formula>\n                      <jats:tex-math>W^r(C,X)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    is nonempty of dimension\n                    <jats:inline-formula>\n                      <jats:tex-math>\\ge \\rho(C,r)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    .\n                  <\/jats:p>\n                  <jats:p>Inequalities for the numerical invariants of curves that do not move linearly on a surface of maximal Albanese dimension are obtained as an application of the previous results.<\/jats:p>","DOI":"10.4171\/jems\/482","type":"journal-article","created":{"date-parts":[[2014,10,29]],"date-time":"2014-10-29T18:45:12Z","timestamp":1414608312000},"page":"2033-2057","source":"Crossref","is-referenced-by-count":6,"title":["Brill\u2013Noether loci for divisors on irregular varieties"],"prefix":"10.4171","volume":"16","author":[{"given":"Margarida","family":"Mendes Lopes","sequence":"first","affiliation":[{"name":"Instituto Superior T\u00e9cnico, Lisboa, Portugal"}]},{"given":"Rita","family":"Pardini","sequence":"additional","affiliation":[{"name":"Universit\u00e0 di Pisa, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2007-2525","authenticated-orcid":false,"given":"Gian Pietro","family":"Pirola","sequence":"additional","affiliation":[{"name":"Universit\u00e0 di Pavia, Italy"}]}],"member":"2673","container-title":["Journal of the European Mathematical Society"],"original-title":[],"link":[{"URL":"http:\/\/www.ems-ph.org\/fulltext\/10.4171\/JEMS\/482","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T13:58:32Z","timestamp":1762869512000},"score":1,"resource":{"primary":{"URL":"https:\/\/ems.press\/doi\/10.4171\/jems\/482"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,10,29]]},"references-count":0,"journal-issue":{"issue":"10"},"URL":"https:\/\/doi.org\/10.4171\/jems\/482","relation":{},"ISSN":["1435-9855","1435-9863"],"issn-type":[{"type":"print","value":"1435-9855"},{"type":"electronic","value":"1435-9863"}],"subject":[],"published":{"date-parts":[[2014,10,29]]}}}