Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 11 of 11 for “"birational geometry"”.
-
Birational geometry of the space of rational curves in homogeneous varieties
In this thesis, we investigate the birational geometry of the space of rational curves in various homogeneous spaces, with a focus on the quasi-map compactification induced by the Quot and Hyperquot functors. We first study the birational geometry of the Quot scheme of sheaves on P1 via techniques …
-
On Berglund-Hübsch-Krawitz Mirror Symmetry
… space. First, we will describe their birational geometry using Shioda maps and prove that so-called alternate mirrors are birational. Next, we will compute algebraic invariants of the orbifolds and their crepant resolutions in the case where they are orbifold K3 surfaces, both over the …
-
CALABI-YAU MANIFOLDS OF TYPE A AND THE CONE CONJECTURE FOR HYPERELLIPTIC VARIETIES
… A in all odd dimension. After that, we study the geometry of Calabi-Yau 3-folds of type A. Thanks to Oguiso and Sakurai, we know that there exist only two families F^A_G of Calabi-Yau 3-folds A/G of type A and each of them corresponds uniquely to a group G which acts freely on A and does not …
-
Ample subschemes and partially positive line bundles
A common theme in algebraic geometry is that geometric properties of an algebraic variety are reflected in the subvarieties that are 'positively embedded' in it. Here the case of subvarieties of codimension one is classical and also fundamental to algebraic geometry: divisors correspond to line …
-
Complements on Log Canonical Fano Varieties and Index Conjecture of Log Calabi-Yau Varieties
… first introduce some basic background theory for birational geometry, including notion of singularities, pairs, complements. We will then cover some backgrounds of (log) Fano and Calabi-Yau varieties. We will also state the main new results in the introduction. The majority of work is then split …
-
Towards birational aspects of moduli space of curves
… has proven itself a central object in algebraic geometry. The past decade has seen substantial progress in understanding its geometry. This has been spurred by a flurry of ideas from geometry (algebraic, symplectic, and differential), topology, combinatorics, and physics. One way of understanding …
-
The topology of terminal quartic 3-folds
… it from the point of view of Mori theory. I use birational geometric methods to obtain these results.
-
Explicit moduli spaces for curves of genus 1 and 2
… pairing to a power of $r$. We first study the birational geometry of the surfaces $Z_{N,r}^{\text{sym}}$ which arise as quotients of the surfaces $Z_{N,r}$ by the involution swapping the roles of the $N$-congruent elliptic curves. Building on previous work of Kani--Schanz and Hermann we compute …
-
Deformation invariance of rational pairs
Rational pairs, recently introduced by Kollár and Kovács, generalize rational singularities to pairs (X,D). Here X is a normal variety and D is a reduced divisor on X. Integral to the definition of a rational pair is the notion of a thrifty resolution, also defined by Kollár and Kovács, and in …
-
C*-actions on rational homogeneous varieties and the associated birational maps
Given a birational map among projective varieties, it is known that there exists a variety Z with a one-dimensional torus action such that the birational map is induced from two geometric quotients of Z. We proceed in the opposite direction: given a smooth projective variety X with a …
-
Higher direct images of ideal sheaves, correspondences in log Hodge cohomology and globally F-full varieties
… ideal sheaves under (a restricted class of) birational morphisms of pairs in arbitrary characteristic, and as an application extends some foundational results in the theory of rational pairs that were previously known only in characteristic 0. Chapter 2 discusses correspondences in …