A Rationality Criterion for Projective Surfaces - Partial Solution to Kollár’s Conjecture
نویسندگان
چکیده
Kollár’s conjecture states that a complex projective surface S with quotient singularities and with H(S, Q) = Q should be rational if its smooth part S is simply connected. We confirm the conjecture under the additional condition that the exceptional divisor in a minimal resolution of S has at most 3 components over each singular point of S.
منابع مشابه
The Auslander-Reiten Conjecture for Group Rings
This paper studies the vanishing of $Ext$ modules over group rings. Let $R$ be a commutative noetherian ring and $ga$ a group. We provide a criterion under which the vanishing of self extensions of a finitely generated $Rga$-module $M$ forces it to be projective. Using this result, it is shown that $Rga$ satisfies the Auslander-Reiten conjecture, whenever $R$ has finite global dimension and $ga...
متن کاملPartial proof of Graham Higman's conjecture related to coset diagrams
Graham Higman has defined coset diagrams for PSL(2,ℤ). These diagrams are composed of fragments, and the fragments are further composed of two or more circuits. Q. Mushtaq has proved in 1983 that existence of a certain fragment γ of a coset diagram in a coset diagram is a polynomial f in ℤ[z]. Higman has conjectured that, the polynomials related to the fragments are monic and for a fixed degree...
متن کاملHomological Projective Duality for Grassmannians of Lines
We show that homologically projectively dual varieties for Grassmannians Gr(2, 6) and Gr(2, 7) are given by certain noncommutative resolutions of singularities of the corresponding Pfaffian varieties. As an application we describe the derived categories of linear sections of these Grassmannians and Pfaffians. In particular, we show that (1) the derived category of a Pfaffian cubic 4-fold admits...
متن کاملAdjoint Line Bundles and Syzygies of Projective Varieties
Let X be a smooth projective variety and let K be the canonical divisor of X. In this paper, we study embeddings of X given by adjoint line bundles K ⊗ L, where L is an ample invertible sheaf. When X is a regular surface, we obtain a numerical criterion for K ⊗ L to have property Np. In particular, we prove Mukai’s conjecture for regular anticanonical surfaces. When X is a regular variety of ar...
متن کاملCalabi-Yau Three-folds and Moduli of Abelian Surfaces II
The main goal of this paper, which is a continuation of [GP1], [GP2] and [GP3], is to describe birational models for moduli spaces Ad of polarized abelian surfaces of type (1, d) for small values of d, and for moduli spaces of such polarized abelian surfaces with suitably defined partial or canonical level structure. We can then decide the uniruledness, unirationality or rationality of nonsingu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005