We present an implementation of the Atiyah-Bott residue formula for $\overline{M}_{0,m}(\mathbb{P}^{n},d)$. use this to compute a large number Gromov-Witten invariants genus $0$, including intersection numbers rational curves on general complete intersections. also some contact satisfying suitable Schubert conditions. Our computations confirm known predictions made by Mirror Symmetry. The code ...

We prove that the Gromov width of any Bott-Samelson variety birational to a Schubert and equipped with rational K\"ahler form equals symplectic area minimal curve. From this, we derive an estimate for Seshadri constants ample line bundles on varieties.

We consider Bott-Samelson varieties BSc(s) for a semisimple compact Lie group C corresponding to sequences of (not necessarily simple) reflections s. Let n be the length s, K maximal torus in and W Weyl C. For any set R not overlapping integer pairs (i,j) such that 1?i?j?n function v:R?W, we subspace BSc(s,v)?BSc(s) solutions equations C/K requiring K-orbit product coordinates counted from i j ...

Abstract Let $\mathsf {C}$ be a symmetrisable generalised Cartan matrix. We introduce four different versions of double Bott–Samelson cells for every pair positive braids in the braid group associated to . prove that decorated are smooth affine varieties, whose coordinate rings naturally isomorphic upper cluster algebras. explicitly describe Donaldson–Thomas transformations on and they transfor...