On the Module of Zariski Differentials and Infinitesimal Deformations of Cusp Singularities.
On the moduli b-divisors of lc-trivial fibrations
Roughly speaking, by using the semi-stable minimal model program, we prove that the moduli part of an lc-trivial fibration coincides with that of a klt-trivial fibration induced by adjunction after taking a suitable generically finite cover. As an application, we obtain that the moduli part of an lc-trivial fibration is b-nef and abundant by Ambro’s result on klt-trivial fibrations.
On the motivic measure on the space of functions.
On the Néron model of jacobians of Shimura curves
On the Néron models of abelian surfaces with quaternionic multiplication.
On the number of compatibly Frobenius split subvarieties, prime -ideals, and log canonical centers
Let be a projective Frobenius split variety with a fixed Frobenius splitting . In this paper we give a sharp uniform bound on the number of subvarieties of which are compatibly Frobenius split with . Similarly, we give a bound on the number of prime -ideals of an -finite -pure local ring. Finally, we also give a bound on the number of log canonical centers of a log canonical pair. This final variant extends a special case of a result of Helmke.
On the period map for abelian covers of projective varieties
On the Picard number of divisors in Fano manifolds
Let be a complex Fano manifold of arbitrary dimension, and a prime divisor in . We consider the image of in under the natural push-forward of -cycles. We show that . Moreover if , then either where is a Del Pezzo surface, or and has a fibration in Del Pezzo surfaces onto a Fano manifold such that .
On the Plurigenera of Minimal Algebraic 3-Folds with K ... 0.
On the Poles of a Local Zeta Function for Curves.
On the p-rank of an abelian variety and its endomorphism algebra.
Let A be an abelian variety defined over a finite field. In this paper, we discuss the relationship between the p-rank of A, r(A), and its endomorphism algebra, End0(A). As is well known, End0(A) determines r(A) when A is an elliptic curve. We show that, under some conditions, the value of r(A) and the structure of End0(A) are related. For example, if the center of End0(A) is an abelian extension of Q, then A is ordinary if and only if End0(A) is a commutative field. Nevertheless, we give an example...
On the Ramification of Branched Coverings of IPn.
On the rationality of certain strata of the Lange stratification of stable vector bundles on curves.
On the singularities of Polar curves.
On the Spannedness and Very Ampleness of Certain Line Bundles on the Blow-ups of IP2C and Fr .
On the string-theoretic Euler numbers of 3-dimensional -- singularities.
On the Structure of the Birational Abel Morphism.
On the superadditivity of secant defects
On the theorem of de Franchis
On the theory of nth power residues and a conjecture of Kronecker