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SUMMARY:Bruno de Oliveira (Miami Univ)
DTSTART:20241108T160000Z
DTEND:20241108T171500Z
DTSTAMP:20260423T024653Z
UID:CIRGET/127
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CIRGET/127/"
 >Chern numbers ratios of surfaces with big cotangent bundle</a>\nby Bruno 
 de Oliveira (Miami Univ) as part of CRM - Séminaire du CIRGET / Géométr
 ie et Topologie\n\nLecture held in PK-5115.\n\nAbstract\nBigness of the co
 tangent bundle of a projective manifold is the condition that the growth o
 f the space of sections of the symmetric powers of the cotangent bundle is
  maximal. The condition implies that the manifold is of general type\, tha
 t is\, its canonical bundle $K_X$ satisfies the same condition. If an alge
 braic surface $X$ has a big cotangent bundle\, then $X$ satisfies Green-Gr
 iffiths-Lang conjecture. This talk examines the implication of our CMS-cri
 terion for bigness of the cotangent  bundle\, a condition about numerical
  invariants of $X$\, towards the possible ratios of the Chern numbers $c_1
 ^2=K_X^2$ and $c_2=\\xi_{top}(X)$ of surfaces $X$ with big cotangent bundl
 e. We present several conjectures concerning  these ratios motivated by t
 he CMS-criterion and  examples supporting the conjectures.\n
LOCATION:https://researchseminars.org/talk/CIRGET/127/
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