Arrangements of rational sections over curves and the varieties they define

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dc.contributor.authorUrzua, Giancarlo
dc.date.accessioned2024-01-10T12:04:18Z
dc.date.available2024-01-10T12:04:18Z
dc.date.issued2011
dc.description.abstractWe introduce arrangements of rational sections over curves. They generalize line arrangements on P-2. Each arrangement of d sections defines a single curve in Pd-2 through the Kapranov's construction of (M) over bar (0,d+1). We show a one-to-one correspondence between arrangements of d sections and irreducible curves in M-0,M-d+1, giving also correspondences for two distinguished subclasses: transversal and simple crossing. Then, we associate to each arrangement A (and so to each irreducible curve in M-0,M-d+1) several families of nonsingular projective surfaces X of general type with Chern numbers asymptotically proportional to various log Chern numbers defined by A. For example, for the main families and over C, any such X is of positive index and pi(1)(X) similar or equal to pi 1 (A), where A is the normalization of A. In this way, any rational curve in M-0,M-d+1 produces simply connected surfaces with Chem numbers ratio bigger than 2. Inequalities like these come from log Chern inequalities, which are in general connected to geometric height inequalities (see Appendix). Along the way, we show examples of etale simply connected surfaces of general type in any characteristic violating any sort of Miyaoka Yau inequality.
dc.format.extent34 páginas
dc.fuente.origenWOS
dc.identifier.doi10.4171/RLM/609
dc.identifier.eissn1720-0768
dc.identifier.issn1120-6330
dc.identifier.urihttps://doi.org/10.4171/RLM/609
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/75757
dc.identifier.wosidWOS:000301399100002
dc.information.autorucMatemática;Urzua G ;S/I;13222
dc.issue.numero4
dc.language.isoen
dc.nota.accesoSin adjunto
dc.pagina.final486
dc.pagina.inicio453
dc.publisherEUROPEAN MATHEMATICAL SOC
dc.revistaRENDICONTI LINCEI-MATEMATICA E APPLICAZIONI
dc.rightsregistro bibliográfico
dc.subjectArrangement of curves
dc.subjectmoduli space
dc.subjectsurface of general type
dc.subjectMiyaoka-Yau inequality
dc.subjectgeometric height inequalities
dc.subjectALGEBRAIC-SURFACES
dc.subjectSTABLE CURVES
dc.titleArrangements of rational sections over curves and the varieties they define
dc.typeartículo
dc.volumen22
sipa.codpersvinculados13222
sipa.indexWOS
sipa.trazabilidadCarga SIPA;09-01-2024
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