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Search: MSC category 14J30 ( $3$-folds [See also 32Q25] )

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1. CJM 2015 (vol 67 pp. 696)

Zhang, Tong
 Geography of Irregular Gorenstein 3-folds In this paper, we study the explicit geography problem of irregular Gorenstein minimal 3-folds of general type. We generalize the classical Noether-Castelnuovo type inequalities for irregular surfaces to irregular 3-folds according to the Albanese dimension. Keywords:3-fold, geography, irregular varietyCategory:14J30

2. CJM 2012 (vol 65 pp. 905)

Thompson, Alan
 Explicit Models for Threefolds Fibred by K3 Surfaces of Degree Two We consider threefolds that admit a fibration by K3 surfaces over a nonsingular curve, equipped with a divisorial sheaf that defines a polarisation of degree two on the general fibre. Under certain assumptions on the threefold we show that its relative log canonical model exists and can be explicitly reconstructed from a small set of data determined by the original fibration. Finally we prove a converse to the above statement: under certain assumptions, any such set of data determines a threefold that arises as the relative log canonical model of a threefold admitting a fibration by K3 surfaces of degree two. Keywords:threefold, fibration, K3 surfaceCategories:14J30, 14D06, 14E30, 14J28

3. CJM 2010 (vol 62 pp. 1293)

Kasprzyk, Alexander M.
 Canonical Toric Fano Threefolds An inductive approach to classifying all toric Fano varieties is given. As an application of this technique, we present a classification of the toric Fano threefolds with at worst canonical singularities. Up to isomorphism, there are $674,\!688$ such varieties. Keywords:toric, Fano, threefold, canonical singularities, convex polytopesCategories:14J30, 14J30, 14M25, 52B20

4. CJM 2010 (vol 62 pp. 1201)

Alzati, Alberto; Besana, Gian Mario
 Criteria for Very Ampleness of Rank Two Vector Bundles over Ruled Surfaces Very ampleness criteria for rank $2$ vector bundles over smooth, ruled surfaces over rational and elliptic curves are given. The criteria are then used to settle open existence questions for some special threefolds of low degree. Keywords:vector bundles, very ampleness, ruled surfacesCategories:14E05, 14J30

5. CJM 2004 (vol 56 pp. 495)

Gomi, Yasushi; Nakamura, Iku; Shinoda, Ken-ichi
 Coinvariant Algebras of Finite Subgroups of $\SL(3,C)$ For most of the finite subgroups of $\SL(3,\mathbf{C})$, we give explicit formulae for the Molien series of the coinvariant algebras, generalizing McKay's formulae \cite{M99} for subgroups of $\SU(2)$. We also study the $G$-orbit Hilbert scheme $\Hilb^G(\mathbf{C}^3)$ for any finite subgroup $G$ of $\SO(3)$, which is known to be a minimal (crepant) resolution of the orbit space $\mathbf{C}^3/G$. In this case the fiber over the origin of the Hilbert-Chow morphism from $\Hilb^G(\mathbf{C}^3)$ to $\mathbf{C}^3/G$ consists of finitely many smooth rational curves, whose planar dual graph is identified with a certain subgraph of the representation graph of $G$. This is an $\SO(3)$ version of the McKay correspondence in the $\SU(2)$ case. Keywords:Hilbert scheme, Invariant theory, Coinvariant algebra,, McKay quiver, McKay correspondenceCategories:14J30, 14J17

6. CJM 2001 (vol 53 pp. 3)

Bell, J. P.
 The Equivariant Grothendieck Groups of the Russell-Koras Threefolds The Russell-Koras contractible threefolds are the smooth affine threefolds having a hyperbolic $\mathbb{C}^*$-action with quotient isomorphic to the corresponding quotient of the linear action on the tangent space at the unique fixed point. Koras and Russell gave a concrete description of all such threefolds and determined many interesting properties they possess. We use this description and these properties to compute the equivariant Grothendieck groups of these threefolds. In addition, we give certain equivariant invariants of these rings. Categories:14J30, 19L47
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