Some New Surfaces of General Type

Some Examples of Smooth Non General Type Surfaces in P4

Some Surfaces of General Type for Which Bloch’s Conjecture Holds

We give many examples of surfaces of general type with pg = 0 for which Bloch’s conjecture holds, for all values of K2 6= 9. Our surfaces are equipped with an involution. Let S be a smooth complex projective surface with pg(S) = 0. Bloch’s conjecture states that the Albanese map A0(S)0 → Alb(S) is an isomorphism, where A0(S)0 is the Chow group of 0-cycles of degree 0 on S. It is known for all s...

Uniruled Surfaces of General Type

We give a systematic construction of uniruled surfaces in positive characteristic. Using this construction, we find surfaces of general type with non-trivial global vector fields, surfaces with arbitrarily non-reduced Picard schemes as well as surfaces with inseparable canonical maps. In particular, we show that some previously known pathologies are not sporadic but exist in abundance.

On Surfaces of General Type

We study nonsingular minimal surfaces of general type with pg = 6 and K2 = 13 whose canonical image is contained in a single nonsingular quadric. We show that under these assumptions, such surfaces are regular and their canonical ideal has codimension 3. Led by Buchsbaum–Eisenbud’s structure theorem, we define a map of S into a weighted Grassmannian, which factors through an embedding of the ca...

Bounding singular surfaces of general type

We provide simpler proofs of several boundedness theorems, contained in in articles [2], [3], for log surfaces of general type with semi log canonical singularities. At the same time, we make these proofs e ective, with explicit upper bounds.