S. J. Sierra
Geometric algebras on projective surfaces.
Wed, 10/28/2009 - 16:01 — SomNambulAuthors: S. J. Sierra
Subjects: Rings and Algebras
AbstractLet X be a projective surface, let \sigma be an automorphism of X, and let L
be a \sigma-ample invertible sheaf on X. We study the properties of a family of
subrings, parameterized by geometric data, of the twisted homogeneous
coordinate ring B(X, L, \sigma). In particular, we find necessary and
sufficient conditions for these subrings to be noetherian. We also study their
homological properties, their associated noncommutative projective schemes, and
when they are maximal orders.A Derived Equivalence For A Del Pezzo Surface Of Degree 6 Over An Arbitrary Field.
Tue, 08/25/2009 - 22:41 — SomNambulAuthors: Mark Blunk, S. J. Sierra, S. Paul Smith
Subjects: Algebraic Geometry
AbstractLet $S$ be a degree six del Pezzo surface over an arbitrary field $F$.
Motivated by the first author's classification of all such $S$ up to
isomorphism in terms of a separable $F$-algebra $B \times Q \times F$, and by
his K-theory isomorphism $K_n(S) \cong K_n(B \times Q \times F)$ for $n \ge 0$,
we prove an equivalence of derived categories $$ \sD^b(\coh S) \equiv
\sD^b(\mod A) $$ where $A$ is an explicitly given finite dimensional
$F$-algebra whose semisimple part is $B \times Q \times F$.
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