János Kollár
Dual graphs of exceptional divisors.
Wed, 03/14/2012 - 15:01 — SomNambulAuthors: János Kollár
Subjects: Algebraic Geometry
AbstractLet p be a singular point of a variety. Consider a resolution where the
preimage of p is a simple normal crossing divisor E. The combinatorial
structure of E is described by a cell complex D(E), called the dual graph or
dual complex of E. It is known that the homotopy type of D(E) depends only on
p, not on the resolution chosen.We prove that this homotopy type can be arbitrary. We also describe which
homotopy types can be obtained from rational singularities.- 4 comments
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Log canonical singularities are Du Bois.
Mon, 12/14/2009 - 16:01 — SomNambulAuthors: János Kollár, Sándor J Kovács
Subjects: Algebraic Geometry
AbstractA recurring difficulty in the Minimal Model Program is that while log
terminal singularities are quite well behaved (for instance, they are
rational), log canonical singularities are much more complicated; they need not
even be Cohen-Macaulay. The aim of this paper is to prove that log canonical
singularities are Du Bois. The concept of Du Bois singularities, introduced by
Steenbrink, is a weakening of rationality. We also prove flatness of the
cohomology sheaves of the relative dualizing complex of a projective family
with Du Bois fibers.Hulls and Husks.
Wed, 09/23/2009 - 13:19 — SomNambulAuthors: János Kollár
Subjects: Algebraic Geometry
AbstractThe aim of this note is to prove an analog of the flattening decomposition
theorem for reflexive hulls. The main applications are: the construction of the
moduli space of varieties of general type, improved flatness conditions and
criteria for simultaneous normalizations.Hulls and Husks.
Wed, 09/23/2009 - 13:19 — SomNambulAuthors: János Kollár
Subjects: Algebraic Geometry
AbstractThe aim of this note is to prove an analog of the flattening decomposition
theorem for reflexive hulls. The main applications are: the construction of the
moduli space of varieties of general type, improved flatness conditions and
criteria for simultaneous normalizations.Lectures on curves on varieties -- Lisbon, 2009.
Mon, 08/31/2009 - 17:16 — SomNambulAuthors: János Kollár
Subjects: Algebraic Geometry
AbstractThese lectures give a short introduction to the study of curves on algebraic
varieties. After an elementary proof of the dimension formula for the space of
curves, we summarize the basic properties of uniruled and of rationally
connected varieties. At the end, some connections with symplectic geometry are
considered.
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