Enumeration of Terracini schemes

TL;DR

This paper presents a method to compute the expected length of Terracini schemes for curves, providing a closed formula for ^4 and discussing higher-dimensional cases.

Contribution

It introduces a way to compute the expected length of Terracini schemes for curves and offers a closed formula for ^4, addressing higher-dimensional varieties.

Findings

Closed formula for curves in ^4

Method to compute expected length of Terracini schemes

Discussion on higher-dimensional varieties

Abstract

In this note we outline a way of computing the expected lenght of the Terracini scheme of a curve, when this scheme is expected to be finite and we give a closed formula for curves in $\p^4$. We also discuss the widely open case of varieties of higher dimension.