ar X iv : m at h / 06 06 65 4 v 3 [ m at h . A T ] 1 J ul 2 00 7 EULER CHARACTERISTICS OF ALGEBRAIC VARIETIES

ar X iv : m at h / 06 06 65 4 v 2 [ m at h . A T ] 1 6 O ct 2 00 6 EULER CHARACTERISTICS OF ALGEBRAIC VARIETIES

The aim of this note is to study the behavior of intersection homology Euler characteristic under morphisms of algebraic varieties. The main result is a direct application of the BBDG decomposition theorem. Similar formulae for Hodge-theoretic invariants of algebraic varieties were announced by the first and third authors in [4, 11].

ar X iv : m at h / 06 07 13 0 v 1 [ m at h . A G ] 5 J ul 2 00 6 TWISTED LOOP GROUPS AND THEIR AFFINE FLAG VARIETIES

ar X iv : m at h / 06 04 33 4 v 1 [ m at h . N T ] 1 4 A pr 2 00 6 Distribution function of values of random Euler products at 1

In the aim of attacking the first conjecture of Montgomery-Vaughan on the distribution of values of the automorphic symmetric power L-functions at 1, we study the distribution function of the truncated random Euler products L(1, sym m g ♮ (ω), y) := p≤y det I − p −1 sym m g ♮ p (ω) −1 , where g ♮ (ω) := {g ♮ p (ω)} p is a sequence of independent random variables, defined in probability space Ω ...

ar X iv : 0 70 7 . 06 78 v 1 [ m at h . A C ] 4 J ul 2 00 7 GENERIC INITIAL IDEALS AND FIBRE PRODUCTS

We study the behavior of generic initial ideals with respect to fibre products. In our main result we determine the generic initial ideal of the fibre product with respect to the reverse lexicographic order. As an application we compute the symmetric algebraic shifted complex of two disjoint simplicial complexes as was conjectured by Kalai. This result is the symmetric analogue of a theorem of ...

ar X iv : m at h / 06 10 30 1 v 1 [ m at h . A G ] 9 O ct 2 00 6 ALGEBRAIC NAHM TRANSFORM FOR PARABOLIC HIGGS BUNDLES ON P

— In this paper, we give a completely algebraic description of Nahm transform for parabolic Higgs bundles on P. 2 KÜRŞAT AKER & SZILÁRD SZABÓ