A remark to a Theorem of Hacon and Pardini

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

Jumping of the nef cone for Fano varieties

Among all projective algebraic varieties, Fano varieties (those with ample anticanonical bundle) can be considered the simplest. Birkar, Cascini, Hacon and McKernan showed that the Cox ring of a Fano variety, the ring of all sections of all line bundles, is finitely generated [4]. This implies a fundamental fact about the birational geometry of a Fano variety: there are only finitely many small...

Some Basic Results on Irregular Varieties Revisited with the Fourier-mukai Transform

Recently Fourier-Mukai methods have proved to be a valuable tool in the study of the geometry of irregular varieties. An especially interesting point is the interplay between the generic vanishing theorems of Green and Lazarsfeld and the notion of generic vanishing sheaves, naturally arising in the Fourier-Mukai context. The purpose of this mainly expository paper is to exemplify this circle of...

A remark on the means of the number of divisors

‎We obtain the asymptotic expansion of the sequence with general term $frac{A_n}{G_n}$‎, ‎where $A_n$ and $G_n$ are the arithmetic and geometric means of the numbers $d(1),d(2),dots,d(n)$‎, ‎with $d(n)$ denoting the number of positive divisors of $n$‎. ‎Also‎, ‎we obtain some explicit bounds concerning $G_n$ and $frac{A_n}{G_n}$.

A short remark on the result of Jozsef Sandor

It is pointed out that, one of the results in the recently published article, ’On the Iyengar-Madhava Rao-Nanjundiah inequality and it’s hyperbolic version’ [3] by J´ozsef S´andor is logically incorrect and new corrected result with it’s proof is presented.