We construct invariants of birational maps with values in the Kontsevich--Tschinkel group
and in the truncated Grothendieck groups of varieties. These invariants are morphisms of …

We discuss a conjecture saying that derived equivalence of smooth projective simply
connected varieties implies that the difference of their classes in the Grothendieck ring of …

Derived equivalence of Ito–Miura–Okawa–Ueda Calabi–Yau 3-folds Page 1 c⃝2018 The
Mathematical Society of Japan J. Math. Soc. Japan Vol. 70, No. 3 (2018) pp. 1007–1013 doi …

We study the intersection of two copies of Gr⁢(2, 5) embedded in ℙ 9, and the intersection of
the two projectively dual Grassmannians in the dual projective space. These intersections …

We exhibit a Cremona transformation of such that the base loci of the map and its inverse
are birational to K3 surfaces. The two K3 surfaces are derived equivalent but not isomorphic …

In this article, we study a spectrum K (V k) such that π 0 K (V k) is the Grothendieck ring of
varieties and such that the higher homotopy groups contain more geometric information …

Based on the method by Küchle (Math Z 218 (4), 563–575, 1995), we give a procedure to list
up all complete intersection Calabi–Yau manifolds with respect to direct sums of irreducible …

This is a survey paper about a selection of results in complex algebraic geometry that
appeared in the recent and less recent litterature, and in which rational homogeneous …

We prove the derived equivalence of a pair of non-compact Calabi–Yau 7-folds, which are
the total spaces of certain rank 2 bundles on G_2 G 2-Grassmannians. The proof follows that …

We construct non‐trivial L‐equivalence between curves of genus one and degree five, and
between elliptic surfaces of multisection index five. These results give the first examples of L …