Related papers: Inversion of adjunction for higher rational singul…
After obtaining some useful identities, we prove an additional functional relation for $q$ exponentials with reversed order of multiplication, as well as the well known direct one in a completely rigorous manner.
We prove Shokurov's index conjecture for quotient singularities.
We determine couples of singular moduli which have rational products
Let $(Z,o)$ be a three-dimensional terminal singularity of type $cA/r$. We prove that all exceptional divisors over $o$ with discrepancies $\le 1$ are rational.
An technically interesting proof of a known theorem.
We prove the converse of Yano's extrapolation theorem for translation invariant operators.
We propose a variant of the effective adjunction conjecture for lc-trivial fibrations. This variant is suitable for inductions and can be used to treat real coefficients.
We give a survey of the Lagrange inversion formula, including different versions and proofs, with applications to combinatorial and formal power series identities.
Higher rational and higher Du Bois singularities have recently been introduced as natural generalizations of the standard definitions of rational and Du Bois singularities. In this note, we discuss these properties for isolated…
We introduce a generalization of the Anderson-Thakur special function, and we prove a rationality result for several variable twisted $L$-series associated to shtuka functions.
We prove the Aharoni Berger Conjecture
We prove a stronger version of a criterion of rationality given by Ionescu and Russo. We use this stronger version to define an invariant for rational varieties (we call it rationality degree), and we classify rational varieties for small…
For the alternating group $A_{6}$ of degree 6, Zassenhaus' conjecture about rational conjugacy of torsion units in integral group rings is confirmed.
A conjecture for higher order separation on generic rational surfaces with some new results about standard divisors.
Using the sign expansion of the surreal numbers, we give a possible notion of convergence for surreal sequences.
A sequence of coefficients that appeared in the evaluation of a rational integral has been shown to be unimodal. An alternative proof is presented.
A mixed type dual to a nondifferentiable variational problem involving higher order derivative is formulated and duality results are proved under generalized invexity conditions. Special cases are generated from our results.
The "Modularity Conjecture" is the assertion that the join of two nonmodular varieties is nonmodular. We establish the veracity of this conjecture for the case of linear idempotent varieties. We also establish analogous results concerning…
We provide a new proof for maximal monotonicity of the subdifferential of a convex function.
We prove a discrete approximation of functionals with jumps and creases.