Susan J. Sierra
Classifying birationally commutative projective surfaces.
Wed, 10/28/2009 - 16:01 — SomNambulAuthors: Susan J. Sierra
Subjects: Rings and Algebras
AbstractLet R be a noetherian connected graded domain of Gelfand-Kirillov dimension 3
over an uncountable algebraically closed field. Suppose that the graded
quotient ring of R is a skew-Laurent ring over a field; we say that R is a
birationally commutative projective surface. We classify birationally
commutative projective surfaces and show that they fall into four families,
parameterized by geometric data. This generalizes work of Rogalski and Stafford
on birationally commutative projective surfaces generated in degree 1; our
proof techniques are quite different.A general homological Kleiman-Bertini theorem.
Mon, 08/24/2009 - 13:10 — SomNambulAuthors: Susan J. Sierra
Subjects: Algebraic Geometry
AbstractLet G be a smooth algebraic group acting on a variety X. Let F and E be
coherent sheaves on X. We show that if all the higher Tor sheaves of F against
G-orbits vanish, then for generic g in G, the sheaf Tor^X_j(gF, E) vanishes for
all j >0. This generalizes a result of Miller and Speyer for transitive group
actions and a result of Speiser, itself generalizing the classical
Kleiman-Bertini theorem, on generic transversality, under a general group
action, of smooth subvarieties over an algebraically closed field of
characteristic 0.
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