Quasismooth hypersurfaces in toric varieties

Abstract

We provide a combinatorial characterization of monomial linear systems on toric varieties whose general member is quasismooth. This is given both in terms of the Newton polytope and in terms of the matrix of exponents of a monomial basis.

Calabi–Yau 3-folds of Picard number 2 with hypersurface Cox rings

“…Applying Lemma 3.14 to w 1 , w 4 , w 5 and T 2 1 T 3 4 yields t | 3. Again Lemma 3.14, this time applied to w 1 , w 2 , w 4 and T 2 1 T 3 3 shows t | 2. Altogether t = 1, thus K is torsion-free.…”

The Anticanonical Complex for Non-degenerate Toric Complete Intersections

“…. , x 6 ) being one of the tuples (1, 1, 1, 1, 1, 1) and (2,2,3,3,3,3,3). As before, we can exclude the second configuration.…”

“…We first take a look at the possible singularities of toric complete intersections and global resolutions of these singularities. The class of singularities we will have to deal with is the following; see also [2]. Definition 4.2.…”