Characterizing projective spaces for varieties with at most quotient singularities
نویسندگان
چکیده
منابع مشابه
Characterizing Projective Spaces for Varieties with at Most Quotient Singularities
We generalize the well-known numerical criterion for projective spaces by Cho, Miyaoka and Shepherd-Barron to varieties with at worst quotient singularities. Let X be a normal projective variety of dimension n ≥ 3 with at most quotient singularities. Our result asserts that if C · (−KX) ≥ n + 1 for every curve C ⊂ X, then X ∼= P .
متن کاملProjective normality of quotient varieties modulo finite groups
In this note, we prove that for any finite dimensional vector space V over an algebraically closed field k, and for any finite subgroup G of GL(V ) which is either solvable or is generated by pseudo reflections such that the |G| is a unit in k, the projective variety P(V )/G is projectively normal with respect to the descent of O(1)⊗|G|.
متن کاملPartitioning Segre varieties and projective spaces
The recent interest both in partitions of finite geometries into other geometric objects and in the classical Segre varieties over finite fields are the background motivation for this paper. More precisely, partitions of Segre varieties into Segre varieties are investigated and the idea of nested partitions is introduced. Other partitions, namely of projective spaces and hyperbolic quadrics, ar...
متن کاملJoins of Projective Varieties and Multisecant Spaces
Let X1, . . . ,Xs ⊂ PN , s ≥ 1, be integral varieties. For any integers ki > 0, 1 ≤ i ≤ s, and t ≥ 0 set ~k := (k1, . . . , ks) and ~ X := (X1, . . . ,Xs). Let Sec( ~ X; t,~k) be the set of all linear t-spaces contained in a linear (k1 + · · · + ks − 1)-space spanned by k1 points of X1, k2 points of X2, . . . , ks points of Xs. Here we study some cases where Sec( ~ X ; t,~k) has the expected di...
متن کاملAll Abelian Quotient C.i.-singularities Admit Projective Crepant Resolutions in All Dimensions All Abelian Quotient C.i.-singularities Admit Projective Crepant Resolutions in All Dimensions
For Gorenstein quotient spaces C d =G, a direct generalization of the classical McKay correspondence in dimensions d 4 would primarily demand the existence of projective, crepant desingularizations. Since this turned out to be not always possible, Reid asked about special classes of such quotient spaces which would satisfy the above property. We prove that the underlying spaces of all Gorenstei...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the Institute of Mathematics Academia Sinica NEW SERIES
سال: 2017
ISSN: 2304-7895,2304-7909
DOI: 10.21915/bimas.2017401